If A is a 3 times 3 matrix and upsilon1upsilon2 y1 y2 are ve

If A is a 3 times 3 matrix and upsilon_1,upsilon_2, y_1, y_2 are vectors so that Ay_1 = upsilon_1 and Ay_2 = upsilon_2 find vector w so that Aw = upsilon_1 + 3upsilon_2.

Solution

Ay1 = v1 ; Ay2 = v2

Aw = v1 +3v2

= Ay1 +3Ay2

Multiply both sides by A^-1

A^-1Aw = A^-1Ay1 + 3A^-1Ay2

w = y1 +2y2