27. Find det(A – 21) if A is the matrix given in Problem 4. -1 4....
Find det(A – 21) if A is the matrix defined in Problem 4. Lin Problem 7 4.
26. Find det(A-21) if A is the matrix defined in Problem 7. 1 1 7. [1]
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).
(a) A is a 4 X4 matrix and 5(A + 1) = 1. Enter det (A + 1). (b) A is a 3 x3 matrix and -A +61 = 0. Enter det (A + 1). (c) A is a 2 X2 matrix and A2 + 2 A – 35 I = 0. If det (A + I)> 0, enter det (A + I).
Problem 1 Consider the matrix Problem 1 Consider the matriz a 2 5 3 11 08 a Find the cofactors C11,C2,C3 of A. b Find the determinant of 1, det(A) [ 2 4 61 Problem 2 Consider the matriz A=008 | 2 5 3 a Use the ero's to put A in upper triangular form 5 Pinul the determinant of A. (A) by keeping track of the row operations in part a and the properties of determinant Problem 3 Consider...
and that C is a 4 x 4 matrix with det(C) = -4. If it is 16 0 0 0 10 -1 0 0 Suppose B = 1 -To 0 – 0 To 0 0 2 possible, evaluate det(C-B). 09 Oo O 36 0-9 0-144 Cannot be determined from the given information
(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) =
4 (1) Find a matrix A „such that (A - 41)-1 3 1 (2) Let A be 3x3 matrix with 4 = 4 Find : (a) det(( 3 A)?(2 A)-') (b) det( 2 A-' + 3 adj (A)) (3)Find the values of a that makes the system has (a) unique solution (b) No Solution. 3 A 7 (4)Find the rank of a matrix 17 0 1 2 (5)Suppose that I : R3 → R2 „such that 2 T (e.) =...
Given the matrix 5 28 -16 A = 1 8 -4 E R3x3, 3 21 -11 1. find all eigenvalues of A, 2. find the corresponding eigenvectors of A 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that 3. show that A is diagonalizable, that is, find an invertible matrix KER3x3, and a diagonal matrix DE R3x3 such that K-IAK = D.
Problem 2. (50 points) Suppose that a 4 x 4 matrix A with rows it. 73, 74, and has determinant det A = 1. Find the following determinants: ☺ U2 ü det 604 det det A +50 Note: You can earn partial creat on this problem Problem 1. (50 points) Let Rem -5 -20 -1 -1 - 1 4 16 0 الها (a) Compute dexA Use Cramer's rule to solve the following system 20x -5x -X -4 3 + 16x9...