Question

B form.

Given the system of equations below, write the system in AX
- 112 - 13y = - 62
72 - 3y = 25
[3]
Il

Answer 1

`X =\begin {bmatrix} -5 & 2\\0 &8\\8 & 1\end{bmatrix}`

Explanation:

`Given \:\: B=\begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix} \: and\: C=\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}`

To Solve: 4X + B = C

`\implies 4X + \begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix}=\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}`

`\implies 4X =\begin {bmatrix} -12 & 6\\-1 & 38\\24 & -6\end{bmatrix}- \begin {bmatrix} 8 & -2\\-1 & 6\\-8 & -10\end{bmatrix}`

`\implies 4X =\begin {bmatrix} -12-8 & 6-(-2)\\-1 -(-1)& 38-6\\24-(-8) & -6-(-10)\end{bmatrix}`

`\implies 4X =\begin {bmatrix} -12-8 & 6+2\\-1 +1 & 38-6\\24+8 & -6+10\end{bmatrix}`

`\implies 4X =\begin {bmatrix} -20 & 8\\0& 32\\32 & 4\end{bmatrix}`

`\implies X =(1)/(4)\begin {bmatrix} -20 & 8\\0& 32\\32 & 4\end{bmatrix}`

`\implies X =\begin {bmatrix} (-20)/(4) & (8)/(4)\\\\(0)/(4)& (32)/(4)\\\\ (32)/(4) & (4)/(4)\end{bmatrix}`

`\implies X =\begin {bmatrix} -5 & 2\\0 &8\\8 & 1\end{bmatrix}`

Answer 2

`X=\left[\begin{array}{cc}-5&2\\0&8\\8&1\end{array}\right]`

Explanation:

Solving the given matrix equation, we find ...

X = (1/4)(C - B)

These operations, subtraction and multiplication by a scalar, are done on a term-by-term basis. A calculator or spreadsheet can do these for you.

For example, the middle right term (row 2, col 2) is ...

(38 -6)/4 = 32/4 = 8