1 2 2 1 -X Find the determinant of the matrix as a formula in terms of x and y. Remember to use the correct syntax for...
Find the determinant of the following matrix as a formula in terms of x and y. Remember to use the correct syntax for a formula: (101) y 01 2 x 1) xy-x
Question 1: Given the following matrix A. 02 A- 1 2 3 2 (a) Find the determinant of A (b) Find eigenvalues and the corresponding eigenspaces of A (c) Determine whether A is diagonalizable. If so, find a matrix P and a diagonal matrix D such that P-1AP=D If not, justify your answer. (d) Find a basis of Im(A) and find the rank of Im(A) (e) Find a basis of Ker(A) and find the rank of Ker(A) Question 1: Given...
U is a 2 x 2 orthogonal matrix of determinant -1. Find 5 · [0, 1] · U if 5 · [1,0] · U = (-3,4]. 2. Let M = [[144, 18], [18, 171]]. Notice that 180 is an eigenvalue of M. Let U be an orthogonal matrix such that U-MU is diagonal, the first column of U has positive entries, and det(U) = 1. Find 145 · U.
1. Use the cofactor expansion formula to calculate the determinant of the following matrix. 1-2 5 2 0 0 0 2 -6 -7 5 5 0 4 4 درا
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2 0 -1 1 b) Decide whether the matrix A has an inverse. If the inverse matrix A-1 exists, find its determinant det(A-1).
Use expansion by cofactors to find the determinant of the matrix. - 3 4 -1 13 1 2 | -1 4 2 Use expansion by cofactors to find the determinant of the matrix. [65 31 0 4 1 00-3]
Dºx-4Dy = 667 1. Consider . Use the determinant of the coefficient matrix (D+2)x+(D+2) y = 81 to solve for x. (Find both x, and x,. Do not solve for y.) (15 pts).
3. Let a >0, and for any A E Rnxn, define Aa aA (a) Prove that for any induced matrix norm, K(Ao) (b) Write the formula for det(Aa) in terms of det(A). estimating well/ill-conditioning of matrices. n(A) . Hint: examine IAall and IAal directly. (c) Based on your result from (a) and (b), comment on whether the determinant is useful for 3. Let a >0, and for any A E Rnxn, define Aa aA (a) Prove that for any induced...
(1 point) Find the determinant of the matrix [1 0 0 -2] M-1 0 3 0 To 3 0 Lo 1 -3 2 o det(M) =
Find the determinant of each matrix: 3 2 A. 1 4 B. -3 2 51 1 4 0 -1 2. 6] 22 2 2 1 C. -4 2. T 0 -9 0 0 2 0 0 0 2. 8. D. 7 | 09 1 0 -4 -36 0 5