Question

Solve this equation for A:

Answer 1

Answer:

$a_{11}=-11$

$a_{12}=-16$

$a_{13}=6$

$a_{14}=-10$

Step-by-step explanation:

Let,

$A=\begin{bmatrix}a_{11} & a_{12} & a_{13} & a_{14}\end{bmatrix}$

We have,

$A+\begin{bmatrix}11 & 17 & -8 & 13\end{bmatrix}=\begin{bmatrix}0& 1& -2& 3\end{bmatrix}$

$\implies \begin{bmatrix}a_{11} & a_{12} & a_{13} & a_{14}\end{bmatrix}+\begin{bmatrix}11 & 17 & -8 & 13\end{bmatrix}= \begin{bmatrix}0 & 1 & -2& 3\end{bmatrix}$

By matrix addition,

$\begin{bmatrix}a_{11}+11 & a_{12}+ 17 & a_{13}-8 & a_{14}+13 \end{bmatrix}= \begin{bmatrix}0& 1 & -2& 3\end{bmatrix}$

By comparing,

$a_{11} + 11 = 0\implies a_{11}=0-11=-11$

$a_{12}+17 = 1\implies a_{12} =1-17= -16$

$a_{13}-8 = -2\implies a_{13} =-2 + 8 =6$

$a_{14}+13 = 3\implies a_{14} = 3 - 13 = -10$

Answer 2

Answer:  a₁₁ = -11      a₁₂ = -16       a₁₃ = 6      a₁₄ = -10

Step-by-step explanation:

"A" represents the following matrix of unknown values [a₁₁    a₁₂      a₁₃     a₁₄]

[a₁₁    a₁₂      a₁₃     a₁₄]   +    [11    17      -8     13]   =     [0   1      -2     3]

a₁₁ + 11 = 0   -->   a₁₁ = 0 - 11    = -11

       a₁₂ + 17 = 1   -->   a₁₂ = 1 - 17    = -16

                   a₁₃ + -8 = -2  -->  a₁₃ = -2 + 8  = 6

                             a₁₄ + 13 = 3   -->  a₁₄ = 3 - 13   = -10