If Then which of the sums A + B, B + C, C + D and B + D is defined?

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

If $A = [\begin{array}{cc} 2 & 3 \\ 1 & 2 \end{array}], B = [\begin{array}{ccc} 1 & 3 & 2 \\ 4 & 3 & 1 \end{array}], C = [\begin{array}{c} 1 \\ 2 \end{array}], D = [\begin{array}{ccc} 4 & 6 & 8 \\ 5 & 7 & 9 \end{array}]$

Then which of the sums A + B, B + C, C + D and B + D is defined?

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Order of the matrix A = 2 × 2, B = 2 × 3, C = 2 × 1 and D = 2 × 3

We know that,

Only the matrices of the same order can be added.

Hence, only B + D is defined as they have same order.