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

Question

asked Oct 9, 2020 35.7k views

2 Answers

Jraufeisen · Answer 1 · 2020-10-15T23:32:46+0000

Answer:

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

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

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