If then x = ___ and y = __

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

If $[\begin{array}{cc} x & 0 \\ 1 & y \end{array}] - [\begin{array}{cc} 2 & - 4 \\ - 3 & - 4 \end{array}] = [\begin{array}{cc} 3 & 5 \\ 6 & 3 \end{array}] - [\begin{array}{cc} 2 & 1 \\ 2 & 1 \end{array}],$ then x = ___ and y = ___.

3, 5

– 3, – 3

3, – 2

– 3, 2

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Given,

[\begin{array}{cc} x & 0 \\ 1 & y \end{array}] - [\begin{array}{cc} 2 & - 4 \\ - 3 & - 4 \end{array}] = [\begin{array}{cc} 3 & 5 \\ 6 & 3 \end{array}] - [\begin{array}{cc} 2 & 1 \\ 2 & 1 \end{array}]

\Rightarrow [\begin{array}{cc} x - 2 & 4 \\ 4 & y + 4 \end{array}] = [\begin{array}{cc} 1 & 4 \\ 4 & 2 \end{array}]

\Rightarrow [\begin{array}{c} x - 2 = 1 \\ y + 4 = 2 \end{array}]

\Rightarrow [\begin{array}{c} x = 1 + 2 \\ y = 2 - 4 \end{array}]

\Rightarrow [\begin{array}{c} x = 3 \\ y = - 2 \end{array}]