Let a be a 5 x 3 matrix, let y be a vector in r3, and let z be a vector in r5. suppose ay = z. what fact allows you to conclude that the system ax = 5z is consistent?

Step by step approach is as shown

Step-by-step explanation:

Consider the system Ax = 5z (1)Recalling that z = AySubstitute (Ay) for z in equation (1)therefore, Ax = 5(Ay) (2) Hence the equation can also be written as Ax = A(5y) (3)

recalling from commutative law that A + B = B + A and since A is a scalar, and from scalar multiplication of matrix.

From equation (3) ; Ax = A(5y), it implies that x = 5y from comparison and as such if we compare with equation (2) where z = Aytherefore equation (2) can then be written as Ax = 5z, since there is consistency as such the the equation will also have a solution.

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