If , then find A + B and B + C.

Engineering

Mathematics

Algebra of Matrices

Question

If $A = [\begin{array}{cc} 2 & 3 \\ 5 & 7 \end{array}], B = [\begin{array}{ccc} - 1 & 0 & 2 \\ 3 & 4 & 1 \end{array}], C = [\begin{array}{ccc} - 1 & 2 & 3 \\ 2 & 1 & 0 \end{array}]$ , then find A + B and B + C.

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$A = [\begin{array}{cc} 2 & 3 \\ 5 & 7 \end{array}], B = [\begin{array}{ccc} - 1 & 0 & 2 \\ 3 & 4 & 1 \end{array}]$ and $C = [\begin{array}{ccc} - 1 & 2 & 3 \\ 2 & 1 & 0 \end{array}]$

⇒ Size of matrix A is 2 × 2 and B is 2 × 3.

⇒ A + B does not exist. We cannot add this matrix because they are not the same size.

⇒

B + C = [\begin{array}{ccc} - 1 & 0 & 2 \\ 3 & 4 & 1 \end{array}] + [\begin{array}{ccc} - 1 & 2 & 3 \\ 2 & 1 & 0 \end{array}]

= [\begin{array}{ccc} - 1 + (- 1) & 0 + 2 & 2 + 3 \\ 3 + 2 & 4 + 1 & 1 + 0 \end{array}]

= [\begin{array}{ccc} - 2 & 2 & 5 \\ 5 & 5 & 1 \end{array}]