Question

Please help!!!

1. Select the best answer for the question.
Multiply matrix D = [5,-2,1 ] by matrix E= [12] A. [4 8] B. 2 C. [5 -2 1 ,10 4 2] D. [5 10, -2 -4, 1 2]

2. Subtract [-6 -4,6 0, 6 4] - [-5 5, -4 -4,6 -4]

3. Add [1 -4,3 5] + [-2 6,-2 4]

4. Find the determinant of A= [ 4 -7, 3 -2]

A. 13
B. −2
C. 2
D. 29


5. What is matrix A + matrix B?
A=[3 0, 2 -1] B= [ 2 8, .6 3]

6. What is 4C?
c= [12 03/2, 1 -6 7]

7. Evaluate the determinant for the following matrix: [-5 1, 5 4]

8. Complete the multiplication: 2EA E= [12] A= [3 0, 2 -1]

9. Multiply [5 0 , 3 -5] x [2 -1, 2 -2]

Answer 1

Question 1:

$\left[\begin{array}{ccc}5\\-2\\1\end{array}\right] \left[\begin{array}{ccc}12\end{array}\right] = \left[\begin{array}{ccc}(5)(12)+(-2)(12)+(1)(1)\end{array}\right]$
= $\left[\begin{array}{ccc}60-24+12\end{array}\right] = \left[\begin{array}{ccc}48\end{array}\right]$
Answer: A
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Question 2
$\left[\begin{array}{ccc}-6&-4\\6&0\\6&4\end{array}\right] - \left[\begin{array}{ccc}-5&5\\-4&-4\\6&-4\end{array}\right]$
$\left[\begin{array}{ccc}(-6--5)&(-4-5)\\(6--4)&(0--4)\\(6-6)&(4--4)\end{array}\right] = \left[\begin{array}{ccc}-1&-9\\10&4\\0&8\end{array}\right]$
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Question 3

$\left[\begin{array}{ccc}1&-4\\3&5\end{array}\right] + \left[\begin{array}{ccc}-2&6\\-2&4\end{array}\right]$
=$\left[\begin{array}{ccc}(1+-2)&(-4+6)\\(3+-2)&(5+4)\end{array}\right]$
=$\left[\begin{array}{ccc}-1&2\\1&9\end{array}\right]$
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Question 4

$A= \left[\begin{array}{ccc}4&-7\\3&-2\end{array}\right]$
$det A=(4)(-2)-(-7)(3)=-8+21=13$

Answer: A
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Question 5
$\left[\begin{array}{ccc}3&0\\2&-1\end{array}\right] + \left[\begin{array}{ccc}2&8\\6&3\end{array}\right]$
=$\left[\begin{array}{ccc}3+2&0+8\\2+6&(-1)+3\end{array}\right]$
=$\left[\begin{array}{ccc}5&8\\8&2\end{array}\right]$
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Question 6
$4 \left[\begin{array}{ccc}12&0& \frac{3}{2} \\1&-6&7\end{array}\right] = \left[\begin{array}{ccc}48&0&6\\4&-24&28\end{array}\right]$

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Question 7

$C = \left[\begin{array}{ccc}-5&1\\5&4\end{array}\right]$
$det C = (-5)(4) - (1)(5) = -20-5 = -25$
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Question 8
$2 \left[\begin{array}{ccc}12\end{array}\right] \left[\begin{array}{ccc}3&0\\2&-1\end{array}\right]$
$\left[\begin{array}{ccc}24\end{array}\right] \left[\begin{array}{ccc}3&6\\2&-1\end{array}\right]$
$\left[\begin{array}{ccc}72&0\\48&-24\end{array}\right]$
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Question 9
$\left[\begin{array}{ccc}5&0\\3&-5\end{array}\right] \left[\begin{array}{ccc}2&-1\\2&-2\end{array}\right]$
$\left[\begin{array}{ccc}(5)(2)+(0)(2)&(5)(-1)+(0)(-2)\\(3)(2)+(-5)(2)&(3)(-1)+(-5)(-2)\end{array}\right]$
$\left[\begin{array}{ccc}10+0&-5+0\\6-10&-3+10\end{array}\right] = \left[\begin{array}{ccc}10&-5\\-4&7\end{array}\right]$