Ghosty190

Feb 24, 2011, 03:59 AM

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 âˆ’ âˆš3x2 + 0, 032x3 = 5

B. 7x1x2 âˆ’ 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 âˆ’ z = 8

3x âˆ’ y + 2z = âˆ’5

4x + 2y + 3z = âˆ’1

A. (1, 2, âˆ’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 rowâ€“echelon form.

B. A is in reduced rowâ€“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 Ã— 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 Ã— 2 matrix, B is an r Ã— s matrix and C is a 4 Ã— 3 matrix. If A^T *B*C is defined, which of the following is true?

1. the size of AT BC is 2 Ã— 3

2. r = 2, s = 5

3. r = 3, s = 4

4. r = 3, s = 5

Question 7

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

1. 2 Ã— 4

2. 2 Ã— 5

3. 5 Ã— 4

4. 4 Ã— 2

Question 8

Suppose A, B and C are invertible n Ã— n matrices.

Which of the following statements is/are true?

A. (ABC)^T = A^T *B^T*C^T

B. (ABC)^âˆ’1 = A^âˆ’1*B^âˆ’1*C^âˆ’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

âˆ’1 0 0

is an elementary matrix.

B. If E1 and E2 are two n Ã— n elementary matrices then E1 Ã— 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!

Here they are:

Question 1

Which of the following is a linear equation/are linear equations in x1, x2 and x3?

A. 2x1 âˆ’ âˆš3x2 + 0, 032x3 = 5

B. 7x1x2 âˆ’ 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 âˆ’ z = 8

3x âˆ’ y + 2z = âˆ’5

4x + 2y + 3z = âˆ’1

A. (1, 2, âˆ’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 rowâ€“echelon form.

B. A is in reduced rowâ€“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 Ã— 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 Ã— 2 matrix, B is an r Ã— s matrix and C is a 4 Ã— 3 matrix. If A^T *B*C is defined, which of the following is true?

1. the size of AT BC is 2 Ã— 3

2. r = 2, s = 5

3. r = 3, s = 4

4. r = 3, s = 5

Question 7

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

1. 2 Ã— 4

2. 2 Ã— 5

3. 5 Ã— 4

4. 4 Ã— 2

Question 8

Suppose A, B and C are invertible n Ã— n matrices.

Which of the following statements is/are true?

A. (ABC)^T = A^T *B^T*C^T

B. (ABC)^âˆ’1 = A^âˆ’1*B^âˆ’1*C^âˆ’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

âˆ’1 0 0

is an elementary matrix.

B. If E1 and E2 are two n Ã— n elementary matrices then E1 Ã— 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!