Question

Solve this equation for A:

A +[ 11 17 -8 13 ] = [ 0 1 -2 3 ]

a11 =
a12=
a13=
a14=

Answer 1

`a_(11)=-11`

`a_(12)=-16`

`a_(13)=6`

`a_(14)=-10`

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

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