If and find the matrix C if 2C = A + B.

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

If $A = [\begin{array}{cc} 3 & 7 \\ 2 & 5 \end{array}]$ and $B = [\begin{array}{cc} - 3 & 2 \\ 4 & - 1 \end{array}]$ find the matrix C if 2C = A + B.

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A + B = [\begin{array}{cc} 3 & 7 \\ 2 & 5 \end{array}] + [\begin{array}{cc} - 3 & 2 \\ 4 & - 1 \end{array}]

A + B = [\begin{array}{cc} 3 - 3 & 7 + 2 \\ 2 + 4 & 5 - 1 \end{array}]

A + B = [\begin{array}{cc} 0 & 9 \\ 6 & 4 \end{array}]

\Rightarrow A + B = 2 C = [\begin{array}{cc} 0 & 9 \\ 6 & 4 \end{array}]

\Rightarrow C = \frac{1}{2} [\begin{array}{cc} 0 & 9 \\ 6 & 4 \end{array}]

\Rightarrow C = [\begin{array}{cc} 0 & \frac{9}{2} \\ 3 & 2 \end{array}]

Thus, the matrix

C = [\begin{array}{cc} 0 & \frac{9}{2} \\ 3 & 2 \end{array}]