MAT 2580 Linear Algebra Fall 2024

Professor Poirier | D710 | Fall 2024

Page 3 of 19

Test #1 solutions problem #6a & #6b

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)

Week 7 checklist

Monday, October 14 to Sunday, October 20

Lessons

WeBWorK

  • Vectors in Space
  • Norm and Distance
  • Dot Product
  • Projections
  • Cross Product (if time)

OpenLab

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