Matrix Multiplication?

because 1 can see & b commute , c & b commute , because know & b both invertible, can simplify matrix equation down to:

ax = cb.

can solve using either gaussian elimination or solving system of linear equations:

4x_1 + 5x_2 = 3
3x_1 + 4x_2 = 12

solving give x_1 = ? , x_2 = 39. deliberately left 1 out because can part second. double-check answer sure got right well.

if still unsure how ax = cb, remember inverse property --> if ax = , invertible can a^{-1}ax = a^{-1}a --> x = i, identity matrix. if still stuck, let me know , work out step-by-step you.

hope able help.

let matrices

=

4 5
3 4

b =

3 0
0 3

c =

1 2
3 4

solve equation

b a^4 bxab = ba b^3 a^2 ca

in group gl2(r) of invertible real 2 × 2-matrices.

hint: note matrices commute.

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