Let A = 2 & -1 3 & 4 , = B = 5 & 2 7 & 4 , C = 2 & 5 3 & 8 ,find … - Vidyadip

Question

$\text{Let A} = \begin{pmatrix} 2 & -1 \\ 3 & 4 \\ \end{pmatrix}, = \text{B} = \begin{pmatrix} 5 & 2 \\ 7 & 4 \\ \end{pmatrix}, \text{C} = \begin{pmatrix} 2 & 5 \\ 3 & 8 \\ \end{pmatrix},$find a matrix D such that CD – AB = O.

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Answer

$\text{Let D} = \begin{bmatrix} \text{x} & \text{y} \\ \text{z} & \text{w}\\ \end{bmatrix}$
$\text{CD} = \text{AB} \Rightarrow\begin{bmatrix} \text{2x + 5z} & \text{2y + 5w} \\ \text{3x + 8z} & \text{3y + 8w}\\ \end{bmatrix} = \begin{bmatrix} 3 & 0 \\ 43 & 22\\ \end{bmatrix}$
$\text{2x + 5z = 3, 3x + 8z = 43; 2y + 5w = 0, 3y + 8w = 22.}$
$\text{Solving, we get x = –191, y = –110, z = 77, w = 44}$
$\therefore \text{D} = \begin{bmatrix} -191 & -110\\ 77 & 44\\ \end{bmatrix}$

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