Friday October 16
START: 16:10
DURATION: 110 mins
University of Toronto
Department of Mathematics
MIDTERM EXAMINATION I
MAT223H1F
Linear Algbera I
EXAMINERS: T. Bazett, I. Biborski, N. Garcia-Fritz, S. Homayouni-Boroojeni, A. Kolpakov, H. Nuchi, S. Uppal

Department of Mathematics, University of Toronto
MAT223H1F - Linear Algebra I
Fall 2015
Tutorial Problems 3
1. Suppose a 3 3 matrix A has inverse
2
0
0
1
5
0
1
1 .
1
1
Find a matrix B such that (AB 4I3 )T A = C, where C = 0
0
2 5
0 1
2. Find all values of

Department of Mathematics, University of Toronto
MAT223H1F - Linear Algebra I
Fall 2015
Tutorial Problems 3
Key terms and ideas:
Here are the key terms and ideas we are trying to demonstrate in this tutorial question set. The page
number refers to the cou

Department of Mathematics, University of Toronto
MAT223H1F - Linear Algebra I
Fall 2015
Tutorial Problems 4
1
1. Let A = 2
1
4
5
3
3
4 . Express both A and A1 as a product of elementary matrices.
2
2. Let x and y be vectors in Rn . The inner (or dot) prod

Department of Mathematics, University of Toronto
MAT223H1F - Linear Algebra I
Fall 2015
Tutorial Problems 3
Key terms and ideas:
Here are the key terms and ideas we are trying to demonstrate in this tutorial question set. The page
number refers to the cou