Which of the following matrices are conformable for addition | ClassNotes

Aug 03, 2022

Question:

Which of the following matrices are conformable for addition?

A =$~\left[ \begin{matrix} 2 & 1 \\ -1 & 3 \\ \end{matrix} \right]$	B =$~\left[ \begin{matrix} 3 \\ 1 \\ \end{matrix} \right]$
C = $\left[ \begin{matrix} 1 & 0 \\ 2 & -1 \\ 1 & -2 \\ \end{matrix} \right]$	D = $\left[ \begin{matrix} 2+1 \\ 3 \\ \end{matrix} \right]$
E = $\left[ \begin{matrix} -1 & 0 \\ 1 & 2 \\ \end{matrix} \right]$	F = $\left[ \begin{matrix} 3 & 2 \\ 1+1 & -4 \\ 3+2 & 2+1 \\ \end{matrix} \right]$

Difficulty: Easy

Solution:

Solving D

D = $\left[ \begin{matrix} 2+1 \\ 3 \\ \end{matrix} \right]$

D = $\left[ \begin{matrix} 3 \\ 3 \\ \end{matrix} \right]$

Solving F

F = $\left[ \begin{matrix} 3 & 2 \\ 1+1 & -4 \\ 3+2 & 2+1 \\ \end{matrix} \right]$

F = $\left[ \begin{matrix} 3 & 2 \\ 2 & -4 \\ 5 & 3 \\ \end{matrix} \right]$

Matrices that are of same order are conformable for addition. So, according to this definition:

(i) Matrices A and E are conformable for addition (because both have order 2-by-2).

(ii) Matrices B and D are conformable for addition (because both have order 1-by-1).

(iii) Matrices C and F are conformable for addition (because both have order 3-by-2).