If on matrices. Find the value of x & y.

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

If $2 [\begin{array}{cc} 3 & 4 \\ 5 & x \end{array}] + [\begin{array}{cc} 1 & y \\ 0 & 1 \end{array}] = [\begin{array}{cc} 7 & 0 \\ 10 & 5 \end{array}]$ on matrices. Find the value of x & y.

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Since the order of the matrices in the L.H.S and R.H.S are the same.

We can add and equate the matrices.

[\begin{array}{cc} 6 & 8 \\ 10 & 2 x \end{array}] + [\begin{array}{cc} 1 & y \\ 0 & 1 \end{array}] = [\begin{array}{cc} 7 & 0 \\ 10 & 5 \end{array}]

[\begin{array}{cc} 6 + 1 & 8 + y \\ 5 + 0 & 2 x + 1 \end{array}] = [\begin{array}{cc} 7 & 0 \\ 10 & 5 \end{array}]

⇒ 8 + y = 0

⇒ y = – 8

⇒ 2x + 1 = 5

⇒ 2x = 5 – 1 = 4

\Rightarrow x = \frac{4}{2} = 2

∴ x = 2, y = – 8