Answers
The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)
How to find the result of a multiplication of two matrices
In this question we must apply the operation of multiplication of two matrices, whose definition is shown below:
[tex]\vec B\, \cdot \, \vec A[/tex], where [tex]\vec B \in \mathbb {R}_{n \times p}[/tex] and [tex]\vec A \in \mathbb{R}_{p \times n}[/tex] (1)
Where each element of the resulting matrix is equal to the following expression:
[tex]c_{(i, j)} = b_{(i, p)} \,\bullet\, a_{(p, j)}[/tex] (2)
Where the operator "[tex]\bullet[/tex]" represents a dot product.
Now we proceed to calculate each element of the matrix:
[tex]c_{(1, 1)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
5 · 1 + 7 · 5 + 3 · (- 1)
37
[tex]c_{(1, 2)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
5 · 7 + 7 · 2 + 3 · 2
55
[tex]c_{(1, 3)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
5 · (- 3) + 7 · 1 + 3 · (- 4)
- 20
[tex]c_{(2, 1)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
(- 3) · 1 + 7 · 5 + 9 · (- 1)
23
[tex]c_{(2, 2)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
(- 3) · 7 + 7 · 2 + 9 · 2
11
[tex]c_{(2, 3)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
(- 3) · (- 3) + 7 · 1 + 9 · (- 4)
- 20
[tex]c_{(3, 1)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
2 · 1 + 5 · 5 + 2 · (- 1)
25
[tex]c_{(3, 2)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
2 · 7 + 5 · 2 + 2 · 2
28
[tex]c_{(3, 3)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
2 · (- 3) + 5 · 1 + 2 · (- 4)
- 9
The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)
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Related Questions
Prove if 5n+3 is odd, then 7n+4 is even
Answers
Evaluate 2(s+t)³-6 when s =3 and t = 2?
Answers
Answer:
244
Step-by-step explanation:
We will see that the evaluated expression is equal to 244.
How to evaluate an expression?Evaluating an expression just means that we need to replace the variables by the wanted numbers.
Here we need to evaluate:
2(s+t)³-6
In t = 2 and s = 3, replacing these in the expression we get:
2(3+2)³- 6 = 2*(5)³ - 6 = 2*125 - 6 = 244
So the evaluated expression is equal to 244.
If you want to learn more about evaluating, you can read:
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How many 1/3 inch cubes does it take to fill a box with width 2 2/3
inches, length 3 1/3 inches, and height 2 1/3 inches?
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Answer:
Step-by-step explanation:
plis ayudaaaaaa que tenga explicación y respuesta pero ayuda plisssss
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Answer:
x=30
Step-by-step explanation:
600/20=30
Percent of Discount
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80%
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Answer:
$96
Step-by-step explanation:
Answer:
The final price after deducting the percent of discount would be $24.
Carsen loves to run. She runs 4 miles each day. If she wants to run a total of 56 miles how many days should she run? Write an equation to show this problem along with the answer. *Please click on "show your work" to set up the problem and show your work. Then, enter your answer in the box to the right. You must complete both of these steps.
Answers
Answer:
56 dived by 4. answer would be 14. so she would need to run two weeks
Step-by-step explanation:
Answer:
14 need to run two weeks
Step-by-step explanation:
write an expression that is equivalent to (x-5)²
Answers
Answer:
x²-10x+25
Step-by-step explanation:
expand the expression
(x-5)²
(x-5)(x-5) distribute
x²-5x-5x+25
combine like terms
x²-10x+25
if you get x^2-25 then you're only squaring the x and 5, you have to square the whole equation (x-5)(x-5) is doing (x-5)^2. for example, if you just had (5)^2 you would take the whole "equation" which is 5 and times that equation by itself.
This is hard please solve it for brainly.
Answers
Answer: C
Step-by-step explanation: you just multiple 40 by 4
Answer:
C) 160
Step-by-step explanation:
multiply each side by 40
the 40 from x/40 is eliminated and then you are left with x = 160
que pasa si un objeto imparable choca con uno inabobible
Answers
English Answer: No object can resist an irresistible force. No force can move an immovable object. So if an immovable object meets an irresistible force it will move and not move.English:
Spanish Answer: Ningún objeto puede resistir una fuerza irresistible. Ninguna fuerza puede mover un objeto inamovible. Entonces, si un objeto inamovible se encuentra con una fuerza irresistible, se moverá y no se moverá.
Step-by-step explanation:
¿Qué pasaría si una fuerza imparable chocara contra un objeto inamovible? Las respuestas comunes a esta paradoja recurren a la lógica y a la semántica.
Lógica: Si existe una cosa tal como una fuerza imparable, entonces no puede existir un objeto inamovible y viceversa. Es lógicamente imposible la existencia de los objetos (una fuerza imparable y un objeto inamovible) en un mismo universo al mismo tiempo.
Semántica: Si existe una cosa tal como una fuerza imparable, entonces hablar de un objeto inamovible no tendría sentido en ese contexto y viceversa, con lo cual el asunto vendría a ser algo así como preguntar, por ejemplo, por un triángulo de cuatro lados.
A circle of a radius r,cm inside a square, so that the circle touches the sides of the square.
a) calculate the area of the shaded region when r=6
Answers
Answer:
30.9 square cm
Step-by-step explanation:
subtract area of circle from area of square
Area of square = 12² or 144
(each side is twice the radius)
Area of circle = 6²π or 113.1
Mika rides his bike 3 miles each way to his friend's house. He leaves his house at 4 p.m. How many miles does he ride his bike there and back? What information is extra?
Answers
Answer:
How many miles does he ride his bike there and back?
6 miles.
What information is extra?
The hour at which he leaves his house.
Step-by-step explanation:
We know that he rides 3 miles each way.
Then he rides 3 miles from his house to his friend's house, and another 3 miles from his friend's house to his house.
So he rides 3 miles both times, if we add that, we get:
3 miles + 3 miles = 6 miles
So:
How many miles does he ride his bike there and back?
6 miles.
And to answer the other question, we need to look at the given information that we did not use in this calculation. In this case, is the hour at which he leaves his house.
Notice that we never did use the fact that he leaves his house at 4 p.m.
Then:
What information is extra?
The hour at which he leaves his house.
4+ 3/6 + 2/6! It’s zearn!!
Answers
Answer:
=29/6
Step-by-step explanation:
4+3/6+2/6
=4+1/2+2/6
=9/2+2/6
=9/2+1/3
=29/6
Answer:
4 5/6 = 29/6 = 4.833333333
Step-by-step explanation:
4+3/6+2/6
Reduce the fraction 3/6 to lowest terms by extracting and canceling out 3.
4+1/2+2/6
Convert 4 to fraction 8/2
8/2+1/2+2/6
Since 8/2 and 1/2 have the same denominator, add them by adding their numerators.
8+1 / 2 + 2/6
Add 8 and 1 to get 9.
9/2 + 2/6
Reduce the fraction 2/6 to lowest terms by extracting and canceling out 2.
9/2 + 1/3
Least common multiple of 2 and 3 is 6. Convert 9/2 and 1/3 to fractions with denominator 6.
27/6 + 2/6
Since 27/6 and 2/6 have the same denominator, add them by adding their numerators.
27+2 / 6
Add 27 and 2 to get 29.
29/6
Any help on this?
Y=3x+7
Y=x+1
Answers
Answer:
The answer is (x,y)=(-3,-2)
Step-by-step explanation:
I used the comparison method because I dont know what type of method you needed, sorry. The methods I know would be: the Comparison Method (what I used), the Substitution Method, Elimination Method,Inverse Matrix Method, Cramer's Rule, and the Gauss-Jordan Method.
You can also rewrite this equation to 3x-y=-7 and x-y=-1.
I'm sorry, I dont know what kind of answer you're looking for. I really hope this helps.
Use the net to find the approximate surface area of the cylinder to the nearest square meter.
Answers
Answer:
Step-by-step explanation:
radius r of cylinder = 7
circumference of cylinder = 2πr = 14π meters.
lateral area of cylinder = 14π×11 = 154π m². This is represented by the rectangle.
area of top = πr² = 49π m²
area of bottom = area of top = 49π m²
total surface area = lateral area + 2(top area) = 154π + 2×49π = 252π ≅ 792 m²
an enrollment of 200 students and this year enrollment has increased by 118%. What is this year's enrollment ?
Answers
Answer:
436 students
Step-by-step explanation:
Original number of students enrolled = 200students
% increase = 118%
Increment = 118% of 200
Increment = 1.18 * 200
Increment = 236
The year enrollment = 200 + 236
The year enrollment = 436 students
1) (1 - 4k) - (7k+5)=
How to simplify?
Answers
Answer:
Step-by-step explanation:
What is the surface area of a rectangular prism that has a length of 13 inches, a width of 7 inches and a height of 11 inches?
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Answer:
91 porq se multiplica 32+54Leo has three pieces of ribbon. One piece is 4 yards long, another piece is 5 feet long, and the last piece is 10 inches long. How much ribbon does Leo have in all?
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An angle measures 170°. Through what fraction of
a circle does the angle turn?
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My answer: i need a graph
Which expression represents the algebraic phrase “eleven less than seven times a number”?
11x - 7
7x-11
11 + 7x
11-7x
Answers
What percent of the shaded checker board squares do not have pieces?
VERY URGENT PLEASE
Answers
The 25% of the shaded checker board has pieces on it.
What percent of the shaded checker board squares do not have pieces?To check that, we need to solve the expression below:
Percent = 100%*(# shaded squares with pieces)/(total # of shaded squares)
There are a total of 32 shaded squares, and in 8 of them we can see pieces, then we can replace these values in the formula above to get:
Percent = 100%*(8/32) = 25%
That is the percent of the shaded checker that has pieces.
Learn more about percentages at:
https://brainly.com/question/843074
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A box contains 20 red balls, 25 white balls, and 55 blue balls. Suppose that 10 balls are selected at random one at a time with replacement; that is, each selected ball is replaced in the box before the next selection is made. Determine the probability that at least one color will be missing from the 10 selected balls.
Answers
Answer:
0.164 = 16.4% probability that at least one color will be missing from the 10 selected balls.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Determine the probability that at least one color will be missing from the 10 selected balls.
Red missing:
Each time, there are 55 + 25 = 80 non-red balls, out of 100. So, in each of the 10 trials, 80% = 0.8 probability of not picking a red ball. The probability that no red ball is picked is given by:
(0.8)^10 = 0.1074
White missing:
55 + 20 = 75 non-white balls, out of 100, in each trial. The probability that no white ball is picked is given by:
(0.75)^10 = 0.0563
Blue missing:
45 non-blue balls, out of 100. The probability that no blue ball is picked is given by:
(0.45)^10 = 0.0003
Total:
0.1074 + 0.0563 + 0.0003 = 0.164
0.164 = 16.4% probability that at least one color will be missing from the 10 selected balls.
help me pls asap!!!!!
Answers
Have a great day!
Answer:
Check x values and Y values along axis'. It does match
Step-by-step explanation:
Figure ABCD is a trapezoid. Find
the value of x.
B.
3x + 2
C
13
4x + 3
А"
D
X= [?]
Answers
Answer: 3
Step-by-step explanation:
I need help please.
Answers
Answer:
Not a function.
Step-by-step explanation:
The vertical line test is when you run a line -vertical or AKA: up and down- through the path of a graph if the line runs through the path more than once, it has failed the vertical line test, and therefore is not a function. The graph in question fails this test, and cannot be a function.
I need help please HeLp
Answers
Answer:
The triangle is 1, since 10 - 1 is 9.
Hope that helps!
Step-by-step explanation:
C. How long is 10% of a 24-hour day?
Answers
Answer:
2.4 hours
Step-by-step explanation:
Answer:
10% OF a 24 hour day is 2.4 hours
Step-by-step explanation:
10x24/100= 2.4
guys i really need help I'm so lost
Answers
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
2 raised to 4 =2×2×2×2 =16. ; 3 raised to 2 =3×3=9.
=16-9-2
=5
That's it , Very easy
please help and good night
Answers
Answer:
(7) n = ⁴/₃
(8) x = -5
(9) d = ³/₂
(10) v = -20
Step-by-step explanation:
(7) [tex]n-\frac{8}{9} = \frac{4}{9}[/tex]
[tex]n-\frac{8}{9} = \frac{4}{9} \\\\Collect \ similar \ terms \ together\\\\n = \frac{4}{9} + \frac{8}{9} \\\\n = \frac{4+8}{9} \\\\n = \frac{12}{9} \\\\n = \frac{4}{3}[/tex]
(8)
[tex]\frac{3}{2} + \ x = -\frac{7}{2}\\\\collect \ similar \ terms \ together\\\\x = -\frac{7}{2} -\frac{3}{2} \\\\x = \frac{-7-3}{2} \\\\x = \frac{-10}{2} \\\\x = -5[/tex]
(9)
[tex]\frac{6}{5} = \frac{d}{(\frac{5}{4} )} \\\\cross \ and \ multiply\\\\5d = 6(\frac{5}{4} )\\\\5d = \frac{30}{4} \\\\d = \frac{30}{4\times 5} \\\\d = \frac{30}{20} \\\\d = \frac{3}{2} \\\\d = 1\frac{1}{2}[/tex]
(10)
[tex]-\frac{1}{8} v = \frac{5}{2} \\\\\frac{-v}{8} = \frac{5}{2} \\\\cross \ and \ multiply\\\\-2v = 40\\\\-v = \frac{40}{2} \\\\-v = 20\\\\v = -20[/tex]
2 Which graph shows a proportional relationship? a b c d
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Answer:
x xjjkdjbdnnxuhxnmdujxnxlxuxbx