Homework Answers
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4. Let A and B be 4 x 4 matrices. Suppose det A= 4 and det(AB)...
4. Let A and B be 4 x 4 matrices. Suppose det A= 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-1)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. [2] and us 6. (6 points) Let vi...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det (A?)? (d) (4 points) What is det(A-?)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. and 2 6. (6 points) Let...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-')? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of A™ are linearly independent. and t = [ ] 6. (6...
It + 3 Solve det - 3 0 0 O for t. t - 4 2...
It + 3 Solve det - 3 0 0 O for t. t - 4 2 Aphr work on your blank sheets of paper You will sub
Linear Algebra:Question 5 [10 points] If A, B, and C are 4×4 matrices; and det(A) =...
Linear Algebra:Question 5 [10 points] If A, B, and C are 4×4
matrices; and det(A) = 4, det(B) = −5, and det(C) = −4 then
compute:
Question 5 [10 points] If A, B, and C are 4x4 matrices; and det(A) = 4, det(B) = -5, and det(C)=-4 then compute: det(2CT A-18-10-1BICI) = 0
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If...
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If the matrix B is obtained from mes the second row to the first, then det(B) = 2. If the matrix C is obtained from A by swapping the first and second rows , then det(C) = 3. If the matrix D is obtained from A by multiplying the first row by 5, then det(D) =
Let A. B, C, D є Mnxn(F), and det(A) 0, AC-CA. Prove that A B det...
Let A. B, C, D є Mnxn(F), and det(A) 0, AC-CA. Prove that A B det ( )) -det(AD CB)
1 01 4. Let A 11. (a) Find ATA, (b) find det (AAT). [10 points 1...
1 01 4. Let A 11. (a) Find ATA, (b) find det (AAT). [10 points 1 2 3 0 5. Calculate the determinant of D 03 [10 points 0 2 0 7 2 1 1 6. Find the inverse of A 1 3 using the method in section 5.3. 10 points
els response. Let B -- [1 1 L2 2. 0 1 31 2. Find det B...
els response. Let B -- [1 1 L2 2. 0 1 31 2. Find det B 1 (a) via reduction to triangular form (b) by cofactor expansion swer) in the textbox below. Only work on your blank sheets of paper. You will submit your 3 (12pt) - T-
0 2 0 Q1) Let A = 1 3 2 2 0 a) Determine all eigenvalues...
0 2 0 Q1) Let A = 1 3 2 2 0 a) Determine all eigenvalues of A. b) Determine the basis for each eigenspace of A c) Determine the algebraic and geometric multiplicity of each eigenvalue. Q2) Let aj, 02, 03, 04, agbe real numbers. Compute ai det 1 1 Q3) Determine all values of x E R such that matrix 4 0 3 х 2 5 A = is invertable. х 0 0 1 0 0 4 0
4. Let A and B be 4 x 4 matrices. Suppose det A= 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-1)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. [2] and us 6. (6 points) Let vi...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det (A?)? (d) (4 points) What is det(A-?)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. and 2 6. (6 points) Let...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-')? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of A™ are linearly independent. and t = [ ] 6. (6...
It + 3 Solve det - 3 0 0 O for t. t - 4 2 Aphr work on your blank sheets of paper You will sub
Linear Algebra:Question 5 [10 points] If A, B, and C are 4×4
matrices; and det(A) = 4, det(B) = −5, and det(C) = −4 then
compute:
Question 5 [10 points] If A, B, and C are 4x4 matrices; and det(A) = 4, det(B) = -5, and det(C)=-4 then compute: det(2CT A-18-10-1BICI) = 0
(3 points) Let A be a 4 x 4 matrix with det(A) = 8. 1. If the matrix B is obtained from mes the second row to the first, then det(B) = 2. If the matrix C is obtained from A by swapping the first and second rows , then det(C) = 3. If the matrix D is obtained from A by multiplying the first row by 5, then det(D) =
Let A. B, C, D є Mnxn(F), and det(A) 0, AC-CA. Prove that A B det ( )) -det(AD CB)
1 01 4. Let A 11. (a) Find ATA, (b) find det (AAT). [10 points 1 2 3 0 5. Calculate the determinant of D 03 [10 points 0 2 0 7 2 1 1 6. Find the inverse of A 1 3 using the method in section 5.3. 10 points
els response. Let B -- [1 1 L2 2. 0 1 31 2. Find det B 1 (a) via reduction to triangular form (b) by cofactor expansion swer) in the textbox below. Only work on your blank sheets of paper. You will submit your 3 (12pt) - T-
0 2 0 Q1) Let A = 1 3 2 2 0 a) Determine all eigenvalues of A. b) Determine the basis for each eigenspace of A c) Determine the algebraic and geometric multiplicity of each eigenvalue. Q2) Let aj, 02, 03, 04, agbe real numbers. Compute ai det 1 1 Q3) Determine all values of x E R such that matrix 4 0 3 х 2 5 A = is invertable. х 0 0 1 0 0 4 0
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