MATH SOLVE

3 months ago

Q:
# If possible, find a matrix B such that AB = A2 + 2A.

Accepted Solution

A:

Answer:[tex]\large\boxed{B=A+2I}[/tex]Step-by-step explanation:It's possible if dimensions of a matrix A and matrix B are n Γ n[tex]AB=A^2+2A\qquad\text{multiply both sides on the left by}\ A^{-1}\\\\A^{-1}AB=A^{-1}A^2+A^{-1}(2A)\qquad\text{we know}\ A^{-1}A=I\\\\IB=A^{-1}A\cdot A+2A^{-1}A\\\\IB=IA+2I\qquad\text{we know}\ IA=A\\\\B=A+2I[/tex]