Homework Answers
Please answer # 22 and 24 hapter 1 Systems of Linear Equations and Matrices *21. Suppose...
Please answer # 22 and 24
hapter 1 Systems of Linear Equations and Matrices *21. Suppose that A is n × m and B is m × n so that AB is n × n. Show that AB is no invertible if n> m. [Hint: Show that there is a nonzero vector x such that AB then apply Theorem 6.] and 22.) Use the methods of this section to find the inverses of the following matrices complex entries: 1- 0...
and Given the matrices _ 551 B B = -22) find BA. m[1 oli
and Given the matrices _ 551 B B = -22) find BA. m[1 oli
3. (10 points) Simultaneous left inverse The two matrices 3 2] and both left-invertible, and have multiple left inverses. Do they have a common left inverse? Explain how to find a 2 × 4 matrix C that...
3. (10 points) Simultaneous left inverse The two matrices 3 2] and both left-invertible, and have multiple left inverses. Do they have a common left inverse? Explain how to find a 2 × 4 matrix C that satisfies CA-CB-1, or determine that no such matrix exists. (You can use numerical computing to find C.) Hint. Set up a set of linear equations for the entries of C. Remark. There is nothing special about the particular entries of the two matrices...
1. Consider the following matrices. A= 1 2 -1 0 3 4 B 2 3-4 5...
1. Consider the following matrices. A= 1 2 -1 0 3 4 B 2 3-4 5 1 and C= -[-1:] Compute each of the following, if it is defined. If an expression is undefined, explain why. (a) (4 points) A+B (b) (4 points) 2B (c) (4 points) AC (d) (4 points) CB
Use MATLAB to write your codes Consider a matrix A with block matrices as follows: A...
Use MATLAB to write your codes Consider a matrix A with block matrices as follows: A = {A-11 A_12 0 A-22] It can be shown that the inverse of A can be calculated by inverse of submatrices if A11, and A22 are squared matrices: A^-1 = [A_11 A_12 0 A_22] = [A6-1 _11 -A^-1 _11 A_12 A^-1 _22 0 A^-1 _22 Now consider a Matrix A with following submatrices: A11 = identity matrix A22 = identity matrix A12 = [12...
3 2 -1 1 Determine whether AT B is invertible Given the matrices A = [...
3 2 -1 1 Determine whether AT B is invertible Given the matrices A = [ 2 -4and B = -1 or not, where AT denotes the transpose of matrix A. 5. 1 -3 2
6. (10 points) Given the two matrices, A and B, compute C when (i)C= A.*B and...
6. (10 points) Given the two matrices, A and B, compute C when (i)C= A.*B and (ii) C=A*B A = [1 O 3; 5 3 8; 2 4 6]; B = [2 3 7; 9 1 5; 8 8 3],
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT....
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT. Give a proof that if A has an inverse, then so does AT. (c) Let A be a 3 x 3 matrix that can be transformed into the identity matrix by perform ing the following three row operations in the given order: R2 x 3, Ri R3, R3+2R1 (i) Write down the elementary...
[4 points Suppose A, B, and Care 5 x 5 matrices with det(A) = -2, det(B)...
[4 points Suppose A, B, and Care 5 x 5 matrices with det(A) = -2, det(B) = 10 and the columns of C are linearly dependent. Find the following or state that there is not enough information: (a) det(10B-) (b) det(AB) (c) det(CA+CB)
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B =...
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [
3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ]
(i) Calculate A + B,
(ii) Calculate AB
(iii) Calculate the inverse of B,
(iv) Calculate the determinant of C.
(b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2)
and (5, −1, 4) respectively.
(i) Show that P Q~ =...
Please answer # 22 and 24
hapter 1 Systems of Linear Equations and Matrices *21. Suppose that A is n × m and B is m × n so that AB is n × n. Show that AB is no invertible if n> m. [Hint: Show that there is a nonzero vector x such that AB then apply Theorem 6.] and 22.) Use the methods of this section to find the inverses of the following matrices complex entries: 1- 0...
and Given the matrices _ 551 B B = -22) find BA. m[1 oli
3. (10 points) Simultaneous left inverse The two matrices 3 2] and both left-invertible, and have multiple left inverses. Do they have a common left inverse? Explain how to find a 2 × 4 matrix C that satisfies CA-CB-1, or determine that no such matrix exists. (You can use numerical computing to find C.) Hint. Set up a set of linear equations for the entries of C. Remark. There is nothing special about the particular entries of the two matrices...
1. Consider the following matrices. A= 1 2 -1 0 3 4 B 2 3-4 5 1 and C= -[-1:] Compute each of the following, if it is defined. If an expression is undefined, explain why. (a) (4 points) A+B (b) (4 points) 2B (c) (4 points) AC (d) (4 points) CB
Use MATLAB to write your codes Consider a matrix A with block matrices as follows: A = {A-11 A_12 0 A-22] It can be shown that the inverse of A can be calculated by inverse of submatrices if A11, and A22 are squared matrices: A^-1 = [A_11 A_12 0 A_22] = [A6-1 _11 -A^-1 _11 A_12 A^-1 _22 0 A^-1 _22 Now consider a Matrix A with following submatrices: A11 = identity matrix A22 = identity matrix A12 = [12...
3 2 -1 1 Determine whether AT B is invertible Given the matrices A = [ 2 -4and B = -1 or not, where AT denotes the transpose of matrix A. 5. 1 -3 2
6. (10 points) Given the two matrices, A and B, compute C when (i)C= A.*B and (ii) C=A*B A = [1 O 3; 5 3 8; 2 4 6]; B = [2 3 7; 9 1 5; 8 8 3],
Algebra of matrices. 3. (a) If A is a square matrix, what does it mean to say that B is an inverse of A (b) Define AT. Give a proof that if A has an inverse, then so does AT. (c) Let A be a 3 x 3 matrix that can be transformed into the identity matrix by perform ing the following three row operations in the given order: R2 x 3, Ri R3, R3+2R1 (i) Write down the elementary...
[4 points Suppose A, B, and Care 5 x 5 matrices with det(A) = -2, det(B) = 10 and the columns of C are linearly dependent. Find the following or state that there is not enough information: (a) det(10B-) (b) det(AB) (c) det(CA+CB)
2. (a) Consider the following matrices: A = [ 8 −6, 7 1] , B = [
3 −5, 4 −7] C = [ 3 2 −1 ,−3 3 2, 5 −4 −3 ]
(i) Calculate A + B,
(ii) Calculate AB
(iii) Calculate the inverse of B,
(iv) Calculate the determinant of C.
(b) The points P, Q and R have co-ordinates (2, 2, 1), (4, 1, 2)
and (5, −1, 4) respectively.
(i) Show that P Q~ =...
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