Question

What is the value of matrix B if A+B=C?

Answer 1

B

Explanation:

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Answer 2

option B

Explanation:

Step 1

A + B = C

`A=\left[\begin{array}{ccc}8&-3\\3&y+2\end{array}\right]`
`+B=\left[\begin{array}{ccc}3x&z+4\\w&1/2y\end{array}\right]`

=

`C=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right]`

Step 2

`\left[\begin{array}{ccc}8+3x&-3+z+4\\3+w&y+2+y/2\end{array}\right]`
`=\left[\begin{array}{ccc}x&2z\\4&y\end{array}\right]`

Step 3

4 equations are form

Equation 1

8 + 3x = x

8 = -2x

x = -4

Equation 2

-3 + z + 4 = 2z

1 + z = 2z

1 = z

z = 1

Equation 3

3 + w = 4

w = 1

Equation 4

y + 2 + y/2 = y

2 + y/2 = 0

4 + y = 0

y = -4

Step 4

`\left[\begin{array}{ccc}3(-4)&1+4\\1&1(-4)/2\end{array}\right]`

`\left[\begin{array}{ccc}-12&5\\1&-2\end{array}\right]`