Given , find the values of x, y, z and w.

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

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

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Given

3 [\begin{array}{cc} 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}]

[\begin{array}{cc} 3 x & 3 y \\ 3 z & 3 w \end{array}] = [\begin{array}{cc} 4 + x & 6 + x + y \\ - 1 + z + w & 2 w + 3 \end{array}]

Comparing terms, we get

3x = 4 + x

2x = 4

x = 2

3y = 6 + x + y

3y = 6 + 2 + y

2y = 8

y = 4

3w = 2w + 3

w = 3

3z = – 1 + z + w

3z = – 1 + 3 + z

2z = 2

z = 1

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