(Solution) - Find a matrix representative for the linear functions a L R2 -(2025 Original AI-Free Solution)

Paper Details

Find a matrix representative for the linear functions
(a) L: R2 ? R2 that maps ei to

and e2 to
(b) M: R2 ? R2 that takes e1 to
and e2 to
and
(c) N: R2 ? R2 that takes
and
(d) Explain why M = N ? L.
(e) Verify part (d) by multiplying the matrix representatives in the proper order.