[Ghosty190]

I have tried to understand the first few but I can't get the rest, and if you don't understand the questions because I typed them wrong then please tell me!
Here they are:

Question 1
Which of the following is a linear equation/are linear equations in x1, x2 and x3?
A. 2x1 − √3x2 + 0, 032x3 = 5
B. 7x1x2 − 4x2 + x3 = 0
1. Only A 2. Only B 3. Both A and B 4. Neither A nor B.
I chose 1.

Question 2
Which of the following is a solution/are solutions of the system
x + 2x − z = 8
3x − y + 2z = −5
4x + 2y + 3z = −1
A. (1, 2, −3)
B. (1, 2, 3)
1. Only A 2. Only B 3. Both A and B 4. Neither A nor B.
I chose 4

Question 3
Suppose
A =
1 2 0 0
0 0 1 0
0 0 0 1
Which of the following statements is/are true?
A. A is in row–echelon form.
B. A is in reduced row–echelon form.
1. Only A 2. Only B 3. Both A and B 4. Neither A nor B.
I chose 2 here.

Question 4
Consider the system
3x + ky = 3
2x + 2y = 5.
The system will have a unique solution when k is
A. not equal to 3.
B. any real number.
1. A only 2. B only 3. Both A and B 4. Neither A nor B.

Question 5
Suppose A is an m × n matrix, where m < n. Which of the following statements is/are true?
A. The nonhomogeneous system Ax = b has at least one solution.
B. The homogeneous system Ax = 0 has infinitely many solutions
1. Only A 2. Only B 3. Both A and B 4. Neither A nor B.
I don't know this one, nor the rest below. Please help!!

Question 6
Suppose A is a 5 × 2 matrix, B is an r × s matrix and C is a 4 × 3 matrix. If A^T *B*C is defined, which of the following is true?
1. the size of AT BC is 2 × 3
2. r = 2, s = 5
3. r = 3, s = 4
4. r = 3, s = 5

Question 7
Suppose A is a 5×2 matrix, B is an r ×s matrix and C is a 4×3 matrix. If A^T *B*C is defined, then the size of B is
1. 2 × 4
2. 2 × 5
3. 5 × 4
4. 4 × 2

Question 8
Suppose A, B and C are invertible n × n matrices.
Which of the following statements is/are true?
A. (ABC)^T = A^T *B^T*C^T
B. (ABC)^−1 = A^−1*B^−1*C^−1
1. Only A 2. Only B 3. Both A and B 4. Neither A nor B.

Question 9
Which of the following statements is/are true?
A.
0 0 1
0 1 0
−1 0 0
is an elementary matrix.
B. If E1 and E2 are two n × n elementary matrices then E1 × E2 is an elementary matrix.
1. Only A 2. Only B 3. Both A and B 4. Neither A nor B.

Question 10
Suppose A is an upper triangular matrix. Which of the following is/are true?
A. A has 0 as entry in each position below the main diagonal.
B. A has 1 as entry in each position above the main diagonal.
1. Only A 2. Only B 3. Both A and B 4. Neither A nor B.

Thanks in advance!

[Unknown008]

I don't understand the first one or the second one. As for the rest, besides 4, I didn't do matrices to such an extent.

4. When do two linear equations not have any solution?

[ebaines]

Ghosty - please do not copy all your homework problems and expect us to solve them for you. You say you tried the first few - please show us your work and where you're getting stuck and we'll be glad to help you through.

One other thing - unfortunately with this site you can not copy and paste special characters (like from a Word file), because they become intelligible. So to follow up please retype the problem out in the "answer" box (not the comment box) so we can read it properly.