Given : . Find the value of x, y, z and w

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

Given : $3 [\begin{array}{ll} x y \\ z w \end{array}] = [\begin{array}{cc} x & 6 \\ - 1 & 2 w \end{array}] + [\begin{array}{cc} 4 & x + y \\ z + w & 3 \end{array}]$ . Find the value of x, y, z and w

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$[\begin{array}{cc} 3 x & 3 y \\ 3 z & 3 w \end{array}] = [\begin{array}{cc} x + 4 & 6 + x + y \\ - 1 + z + w & 3 + 2 w \end{array}]$
3x = x + 4 ⇒ 2x = 4 ⇒ x = 2
3y = 6 + x + y ⇒ 3y = 6 + 2 + y (putting the value of x)
⇒ 3y = 8 + y ⇒ 2y = 8 ⇒ y = 4
3w = 3 + 2w ⇒ w = 3
3z = – 1 + z + w putting the value of w
3z – z = – 1 + 3 ⇒ 2z = 2 ⇒ z = 1
∴ x = 2 x = 4 z = 1 w = 3

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