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Question 7 [10 points) Find conditions on k that will make the matrix A invertible. To...
Question 14 [10 points] Given the following matrix A, find an invertible matrix U so that A is equal to UR, when R is the reduced row-echelon form of A: You can resize a matrix (when appropriate) by clicking and dragging the bottom right corner of the matrix. 5 -10 5 50 -15 A = 2 -3 1 17 -5 -1-24 7 -3 4 000 000 00 0 Question 14 [10 points] Given the following matrix A, find an invertible...
Question 12 [10 points] Find an invertible matrix P and a diagonal matrix D such that P-lAP=D. | 9 6 -2 A= -20 -13 4 | -24 -12 3 Tooo oool P= 0 0 0 D = 0 0 0 0 0 0 | 0 0 0 Official Time: 19:51:55 CS Scanned with CamScanner
Question 2 [10 points] Find an invertible matrix P and a diagonal matrix D such that P-AP=D. [ 13 0 5 0 -12 0 0 6 1-30 0 -12 0 | 32 0 10 -3) A = 1 P= To o o o 0 0 0 0 0 0 0 0 0 0 0 0 0 o o o o 0 0 0 0 0 0 0 0 0 0 0 0
Question 1 [10 points] Given the following matrices A and B, find an elementary matrix E such that B- EA You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrbx. 4 6-6 0 7 0 5-2 -4 -7 1-10 -4 6-6 0 4 -4 9-3 4 -4 9-3 o 0 0 E- 0 0 0
Question 7 [10 points] For the matrix A below, find a value of k so that A has two basic eigenvectors associated with the eigenvalue 1 - -1. A = 293 6 0-1 4k 0 0 -3 -2 0 0 0 -1 k = 0
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...
Question 4 [10 points] Find a formula in terms of k for the entries of A", where A is the diagonalizable matrix below and PAP-D for the matrices P and D below.
Find all values of k that make the fol- Problem 7 lowing matrix singular: [i 20 k] 1 1 k k2 1 0 1 k 0 1 1 2
Question A matrix of dimensions m × n (an m-by-n matrix) is an ordered collection of m × n elements. which are called eernents (or components). The elements of an (m × n)-dimensional matrix A are denoted as a,, where 1im and1 S, symbolically, written as, A-a(1,1) S (i.j) S(m, ). Written in the familiar notation: 01,1 am Gm,n A3×3matrix The horizontal and vertical lines of entries in a matrix are called rows and columns, respectively A matrix with the...
Question 5 True of False part II: 5 problems, 2 points each. (6). Let w be the x-y plain of R3, then wlis any line that is orthogonal to w. (Select) (7). Let A be a 3 x 3 non-invertible matrix. If Ahas eigenvalues 1 and 2, then A is diagonalizable. Sele (8). If an x n matrix A is diagonalizable, then n eigenvectors of A form a basis of " [Select] (9). Letzbean x 1 vector. Then all matrices...