Question

Use matrix addition to solve this equation: B + 15 −7 4 0 1 2 = 1 2 12 4 0 2 b11 = b12 = b13 = b21 = 4 b22 = −1 b23 = 0

Answer 1

-14

9

8

Explanation:

edge 2021

Answer 2

`b_(11)=-14,b_(12)=9,b_(13)=8,b_(21)=4,b_(22)=-1,b_(23)=0`

Explanation:

The given matrix addition is

`B+\begin{bmatrix}15&-7&4\\ 0&1&2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}`

We need to find the elements of matrix B.

Let
`B=\begin{bmatrix}b_(11)&b_(12)&b_(13)\\ b_(21)&b_(22)&b_(23)\end{bmatrix}`

Substitute the value of matrix.

`\begin{bmatrix}b_(11)&b_(12)&b_(13)\\ b_(21)&b_(22)&b_(23)\end{bmatrix}+\begin{bmatrix}15&-7&4\\ 0&1&2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}`

After addition of two matrix we get

`\begin{bmatrix}b_(11)+15&b_(12)-7&b_(13)+4\\ b_(21)+0&b_(22)+1&b_(23)+2\end{bmatrix}=\begin{bmatrix}1&2&12\\ 4&0&2\end{bmatrix}`

On equating both sides.

`b_(11)+15=1\Rightarrow b_(11)=-14`

`b_(12)-7=2\Rightarrow b_(12)=9`

`b_(13)+4=12\Rightarrow b_(13)=8`

`b_(21)+0=4\Rightarrow b_(21)=4`

`b_(22)+1=0\Rightarrow b_(22)=-1`

`b_(23)+2=2\Rightarrow b_(23)=0`

Therefore, the elements of matrix B are
`b_(11)=-14,b_(12)=9,b_(13)=8,b_(21)=4,b_(22)=-1,b_(23)=0`.