MAT 211 Introduction to Linear Algebra
Spring 2011
Midterm 2
This exam is 80 minutes long. You may not use your notes, textbook or
calculator. Show your work. Good luck!
Problem 1. 20 points. Let V be the subspace of R4 dened by the equation
x1 x2 + 2x3 +
MAT 211 Introduction to Linear Algebra
Spring 2011
Midterm 2
This exam is 80 minutes long. You may not use your notes, textbook or
calculator. Show your work. Good luck!
Problem 1. 20 points. Find the matrix B of the linear transformation
T (x) = Ax with
Topics for 2nd midterm
Chapter 3.3: Dimension of a subspace of Rn , rank-nullity theorem,
nding the basis for the kernel and the image of a linear operator.
Chapter 3.4: Coordinates of a vector in Rn with respect to a basis.
The B -matrix of a linear tr
Practice Midterm 1
Problem 1. Use GaussJordan elimination to nd all solutions of the following linear system:
x1
+
x2
3x1 + 4x2
x2
2x3
3x3
6x3
+ 3 x3
+ 4 x4
x4
+ 8 x4
+ 4 x4
= 8
=6
=0
= 12
Problem 2. Let A, B and C be the following matrices:
4 1
12
2
MAT 211 Introduction to Linear Algebra
Spring 2011
Midterm 2
This exam is 80 minutes long. You may not use your notes, textbook or
calculator. Show your work. Good luck!
Problem 1. 20 points. Find the matrix B of the linear transformation
T (x) = Ax with
MAT 211 Introduction to Linear Algebra
Spring 2011
Midterm 2
This exam is 80 minutes long. You may not use your notes, textbook or
calculator. Show your work. Good luck!
Problem 1. 20 points. Let V be the subspace of R4 dened by the equation
x1 x2 + 2x3 +