yannlamontagne/cegep_linear_algebra_problems

An open source collection of CEGEP level linear algebra problems

cegep_linear_algebra_problems's Issues

Problem 1.1.8 e.

The answer for the elementary row operation needed to match row 3 of Matrix B with row 3 of Matrix A is incorrect because it uses a double sided arrow (↔) instead of a single sided arrow. The operation itself is correct its just the arrow that is incorrect.

Possible mistakes: 2.1.23 i,j 2.1.25j, 2.2.2

2.1.21 (a)

The question asks to find the trace of a given square matrix. The diagonal components are 4,0,-5. The answer given is -9 but it should be -1 as there is no negative sign on the 4.

1.2.5p solution

I think the solution of the RREF matrix in problem 1.2.5p is wrong. I got x1=0, x2=13/3 and x3=4/3. I double-checked online and some math-help websites got the same answer.

Supplementray Problems for 201-NYC-05 Question 5.12

For part a) of this question, I believe the answer should be 5x-6y-2x+13=0 instead of 5x-6y-2x-13=0.

Supplementary Problems for 201-NYC-05 Question 2.4.8

The answer is incorrect for the following reasons:

1. The product of the matrices does not yield the desired matrix
2. Matrix 3 is not an elementary matrix

Solution:
Matrix 3 should be [1 0 0 | 1 1 0 | 0 0 1]

1.2.13 b)

For b), (x1, x2, x3) should be equal to (-3, 1, 4). I think that a retranscription mistake occurred because the matrix in reduced-row echelon form in section a) agrees with what I am saying. Also, when I plug in the values (-3, 1, 4) in the different equations, it gives me the right constants at the end. On the other hand, when I try with (-3, 2, 4), it does not give me the correct constants.

Question 2.1.3 (GH)

Value of point a12 should be positive 1 rather than negative 1.

attached is a file with the solutions I have found to be correct

Section 1.2 #27 b)

b) a & b when no solution -> a^2 -1=0 & ba-b can't =0

The pdf answers are a=-1 and b=all real numbers, but this is impossible because the matrix shows that b can't =0.

If b=0, ba-b=0 (0(anything)-0=0). It is impossible to create a row of zeros with a non-zero in the constant column this way, resulting in consistent solutions regardless of the value of a.

b can't equal all real numbers when it can't equal 0.

Supplementary Problems for 201-NYC-05 Question 4.2

I think that the answer for part d) of question 4.2 should be that the lines are the same and not just parallel. I came to this conclusion by determining that each line passes through the point used to define the equation of the other line. Since this is the case, and their direction vectors are multiples of one another, then I think both lines are identical.