MATH 152 PRACTISE PROBLEMS FOR MIDTERM 2
(1) Find the inverse of the matrix
3 5
1
2
7 6
1 4 2
(2) For what value(s), if any, is the matrix
1 1 a
1 1 2
1 0 5
invertible?
(3) For what value of b is the matrix
1 1 a
A = 1 1 2
1 b 5
invertible for every value
MATH 152 PRACTICE PROBLEMS FOR MIDTERM 1
(1) Find the value of cos where is the angle between the vectors
a = (1, 2, 9)
b = (1, 4, 1)
(2) Find the area of the triangle formed by the three points
(1, 2, 1) (0, 5, 1) (2, 3, 7)
(3) If (1, 1, 1) and (2, 3, 7)
MATH 152 REVIEW PROBLEMS
(1) Suppose that T : R2 R3 is a linear transformation satisfying
2
1
T = 1
4
3
0
2
T = 4
6
2
Find T [ 0 ].
1
(2) Given the transition matrix
3
4
1
4
3
4
1
4
,
nd the equilibrium probability.
(3) Find the determina
UBC Mathematics 152 Midterm I Answer to Version B Q.B3
Solution:
(a) In the parametric formula for L, the direction is the vector multiplied by the parameter
1
lL = 5
2
(b) Similarly, the direction of line M is
lM
2
= 10 = 2lL .
4
Thus, lL and lM are
UBC Mathematics 152 Section 206
Midterm Exam I (Feb 10, 2012)
Instructor: Yue-Xian Li
Answers
Duration: 50 min
I.
(30 marks)
Consider the plane P dened by x 2y + z = 1. (No intermediate step required in
(a), (b), (d).
(a) Find its normal direction n.
(b)
Math 152, Spring 2008, Practise Test #1
This test was given in 2006. It was given slightly earlier in the term and so does not have any material on linear systems on it. Your test #1 may include basic material on solving linear systems. Marks are indicat
The Check Column
Ordinary arithmetic errors are a big problem when you do row operations by hand.
There is a technique called the check column (that is modeled after the parity bit in
computer hardware design) which provides a very eective way to catch me