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![[ 1 0 1] - (3 marks) Let A = -14 2 1 . Determine all values of q for which A is nonsingular. IO 1 q](http://img.homeworklib.com/questions/4d481ca0-a9d8-11eb-bea9-edac52a7e696.png?x-oss-process=image/resize,w_560)
Homework Answers
![Solution: a) Given A={12 ri27 1. R2 R2 =R, 0 [12. AE [173 $ 1) = 6 3] 6:46 = Cip 3355 A = [68] Re-R2 1 / 7 GA = I RR, 2h2 3](http://img.homeworklib.com/questions/4dd93fd0-a9d8-11eb-a8ed-2bd5d86103eb.png?x-oss-process=image/resize,w_560)
(2 points) Let (2 points) Let A=[% ] () Write A as a product of 4...
(2 points) Let (2 points) Let A=[% ] () Write A as a product of 4 elementary matrices: A (ii) Write A-' as a product of 4 elementary matrices: - THE -1
Let A = [111] 1 2 3. Write A as the product of elementary matrices. (1...
Let A = [111] 1 2 3. Write A as the product of elementary matrices. (1 4 5
[M2] Let -1] 2 A = 2 1 -2 3 (a) Find A-1, (b) Use the...
[M2] Let -1] 2 A = 2 1 -2 3 (a) Find A-1, (b) Use the inverse matrix above to solve the system -2x1 + 2x2 – x3 2, X1 + x2 + 2x3 = -1, 2^1 — 2л2 + 3х3 — 5. (c) Write the following matrix A as a product of elementary matrices. |0 A = |1 -2 0 3 5
2. (15 pts; 8,7) Let (a) Find the inverse of the matrix X. (b) Write X-1...
2. (15 pts; 8,7) Let (a) Find the inverse of the matrix X. (b) Write X-1 as a product of elementary matrices. (You only need to give the list of elementary matrices in the right order. There is no need to multiply them out. )
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A...
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A using the cofactor expansion technique along (a) row 1 and (b) column 3. (ii) In trying to find the inverse of A, applying four elementary row operations reduces the aug- mented matrix [A1] to -2 0 0 0 0 -2 2 1 3 0 1 0 1 0 -2 Continue with row reductions to obtain the augmented matrix [1|A-') and thus give the in-...
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each e...
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each eigenspace of A (you may find an orthonormal basis by inspection or use the Gram-Schmidt algorithm on each eigenspace) (c) (2 marks) Deduce that A is orthogonally diagonalizable. Write down an orthogonal matrix P and a diagonal matrix D such that D P-AP. (d) (1 mark) Use the fact that P is an orthogonal matrix to find P-1 (e) (2 marks)...
Previous Answers LarLinAlg8 2.4.029. My Notes Ask Your Teacher A O1/1 points Find a sequence of...
Previous Answers LarLinAlg8 2.4.029. My Notes Ask Your Teacher A O1/1 points Find a sequence of elementary matrices whose product is the given nonsingular matrix. Need Help? Read It Talk to a Tutor 1/1 points | Previous Answers LarLinAlg8 2.4.013. Ask Y 2. My Notes Find a sequence of elementary matrices that can be used to write the matrix in row-echelon form 0 1 2 9 18 0 1 1 0 1 T 0 1 01 0 1 0 1...
Let A and B be square matrices of order 3 such that |A| = 4 and...
Let A and B be square matrices of order 3 such that |A| = 4 and |B| = 7 (1) Find |AB|. (2) Find |2A|. (3) Are A and B singular or nonsingular? Explain. (A) A and B are both singular because they both have nonzero determinants. (B) A and B are both nonsingular because they both have nonzero determinants. (C) A is singular, but B is nonsingular because |A| < |B|. (D) B is singular, but A is nonsingular...
HW10P5 (10 points) Let A be the matrix A =13 5 0 (3 pts) Find the...
HW10P5 (10 points) Let A be the matrix A =13 5 0 (3 pts) Find the elementary matrices that perform the following row operations in sequence: a. 21 * 2 2. E31 : R3 R1R3 b. (3 pts) Show that the elementary matrices you found in (a) can be used as elimination matrices to determine the upper triangular, U, matrix of A. (4 pts) Find the lower triangular, L, matrix that verifies A C. = LU.
linear algbra 2. Let A, B be the following 3 x 3 matrices: A= C? 1...
linear algbra
2. Let A, B be the following 3 x 3 matrices: A= C? 1 0 5 0 2 - 2 1 1 4 B= 1 0 5 0 2 -2 1 1 0 (a) Show that A is not invertible. (b) Identify Nul(A). (e) Determine whether or not B is invertible and identify Nul (B).
(2 points) Let (2 points) Let A=[% ] () Write A as a product of 4 elementary matrices: A (ii) Write A-' as a product of 4 elementary matrices: - THE -1
Let A = [111] 1 2 3. Write A as the product of elementary matrices. (1 4 5
[M2] Let -1] 2 A = 2 1 -2 3 (a) Find A-1, (b) Use the inverse matrix above to solve the system -2x1 + 2x2 – x3 2, X1 + x2 + 2x3 = -1, 2^1 — 2л2 + 3х3 — 5. (c) Write the following matrix A as a product of elementary matrices. |0 A = |1 -2 0 3 5
2. (15 pts; 8,7) Let (a) Find the inverse of the matrix X. (b) Write X-1 as a product of elementary matrices. (You only need to give the list of elementary matrices in the right order. There is no need to multiply them out. )
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A using the cofactor expansion technique along (a) row 1 and (b) column 3. (ii) In trying to find the inverse of A, applying four elementary row operations reduces the aug- mented matrix [A1] to -2 0 0 0 0 -2 2 1 3 0 1 0 1 0 -2 Continue with row reductions to obtain the augmented matrix [1|A-') and thus give the in-...
5. Let (a) (2 marks) Find all eigenvalues of A (b) (4 marks) Find an orthonormal basis for each eigenspace of A (you may find an orthonormal basis by inspection or use the Gram-Schmidt algorithm on each eigenspace) (c) (2 marks) Deduce that A is orthogonally diagonalizable. Write down an orthogonal matrix P and a diagonal matrix D such that D P-AP. (d) (1 mark) Use the fact that P is an orthogonal matrix to find P-1 (e) (2 marks)...
Previous Answers LarLinAlg8 2.4.029. My Notes Ask Your Teacher A O1/1 points Find a sequence of elementary matrices whose product is the given nonsingular matrix. Need Help? Read It Talk to a Tutor 1/1 points | Previous Answers LarLinAlg8 2.4.013. Ask Y 2. My Notes Find a sequence of elementary matrices that can be used to write the matrix in row-echelon form 0 1 2 9 18 0 1 1 0 1 T 0 1 01 0 1 0 1...
HW10P5 (10 points) Let A be the matrix A =13 5 0 (3 pts) Find the elementary matrices that perform the following row operations in sequence: a. 21 * 2 2. E31 : R3 R1R3 b. (3 pts) Show that the elementary matrices you found in (a) can be used as elimination matrices to determine the upper triangular, U, matrix of A. (4 pts) Find the lower triangular, L, matrix that verifies A C. = LU.
linear algbra
2. Let A, B be the following 3 x 3 matrices: A= C? 1 0 5 0 2 - 2 1 1 4 B= 1 0 5 0 2 -2 1 1 0 (a) Show that A is not invertible. (b) Identify Nul(A). (e) Determine whether or not B is invertible and identify Nul (B).
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