Category: Test #1 Solutions (Page 1 of 2)

6(a). True – The transpose of an invertible matrix is an invertible matrix
Ex:

A=

det(A) = -2*-1/2 – 3/2 = -1/2

A^T=

det(A^T) = -2*-1/2 – 3/2 = -1/2

6(b). False – Every system of linear equations has exactly one solution

Infinite Solutions:

x+y=1, 2x+2y=2

2x+2y=2 is basically x+y=1 when divided by 2.

Graph:

No Solutions:

x+y=0, x+y=1

One Solutions:

x+2y=1, 2x+2y=2

Intersects at (1,0)