Let M = [1 –2] and N = Dotes NM exist ? Give reasons.

Engineering

Mathematics

Introduction to Matrix

Algebra of Matrices

Question

Let M = [1 –2] and N = $[\begin{array}{cc} 2 & 1 \\ - 1 & 2 \end{array}] .$
Dotes NM exist ? Give reasons.

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$NM = {[\begin{array}{cc} 2 & 1 \\ - 1 & 2 \end{array}]}_{2 \times 2} {[1 - 2]}_{1 \times 2}$

In order for matrix multiplication to be defined, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

Since 2 ≠ 1

NM does not exist.