-x -1 -x (d) Let A = 2 2 1 2 (i) (ii) Determine an expression for det(A). For what values of x will the matrix be singular? (e) Find det (A) 2 3 4 5) 1 A = 3 2 4 5 3 4 1 4 2 3 5.

Q: Let A and B be square matrices of order 4 such that |A| = -4 and |B| = -4. Find the following. (a)…

A:

Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: (iv). Find det(A¯1) of the following matrix: 1 3 -1 2 1

A:

Q: 3. (a) Solve the matrix equation for X: -1 0 1 1 2 1 1 -3 1 -1 3 1 -1

A: If Ais a m×n matrix and B is a n×p, then AB is m×p Hence here X is 2×3 Let X = abcdef Thus…

Q: 2. (i) Find a matrix X such that (ii) Find a matrix Y such that 1 - 32] x = [3] X -2 21 53 Y = 0 2²…

A:

Q: First question: Find the inverse and determinate of the matrix A = [??H] -1-3 1 3 60 1 0 1 ||

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Q: [x__3y] [x_2y_ 9. Find the inverse of the matrix:

A:

Q: Assuming that all matrices are n x n and invertible, solve for D. CABT DACTB = CAT.

A:

Q: 20. The following are rules of transposition of a matrix except: (explain) a. (A")" = A b. (A + B)"…

A:

Q: Table Q4(b) is generated from the function f(x)=e* – 4x² + B , where B is the last two digits of…

A: here question has a mistake , though I correct it and solve it for you, here two different f(x) is…

Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: Express the linear function as F(x) = CX for some matrix C. f(x1,x2,x3,x4) = (5x3 - x1, 2x3 + x4,…

A:

Q: True or false. Please explain your answer. Let A and B be two nxn matrices. a) b) c) d) If B is a…

A: Let A be a mxn matrix, To Check and explain: whether the following statements are correct or not.…

Q: 3. Let A, B € Mnxn (F) be n x n matrices. (a) Prove that tr(A + B) = tr(A) + tr(B). (b) Prove that…

A: Trace of matrices is sum of its  diagonal entries

Q: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

Q: Q(x1,X2, x3) = 2xỉ + 3x3 – x + 5x1x3 + X2X3

A: Given,        Q(x1, x2, x3)=2x12+3x22-x32+5x1x3+x2x3

Q: Use the inverse matrices to find (AB)-1, (AT)-1, and (2A)-¹. 1-2 ----C -1 A-¹ = B-1 -2 5 (a) (AB)-¹…

A: To find:  and .

Q: Solve for x, y, z, and win the matrix equation (X, Y, Z, W) wx 2 {]+=[xx]-

A:

Q: 4. Determine if the following sets are linearly independent or linearly dependent. Justify your…

A:

Q: (b) Use the adjoint method to obtain the inverse matrix of P and hence. solve the system of linear…

A: Introduction: The transposition of the cofactor matrix for a given matrix is known as the adjoint of…

Q: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

A:

Q: -*₁+3x₂ = 2 2x1 + x2 + 4x3 = 3 x₂ + 2x3 = 4 (a) Using [IA]~ [A¹1], Find A-¹. (b) Find Adj A.…

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: 3 1 Let A Solve the matrix equation -3 -1 XA - X = 2AT + I for X.

A: To solve the matrix equation XA-X=2A^T+I

Q: Solve the matrix equation for X: 1 -1 2 – 15 -3 | 0 1| 8 -5 11 i i X =

A:

Q: 3.) Find the inverse matrix? 2 Use the adjugate of A = 0 -2 1 to find A-1 | 1 0 0 - 2 3.

A:

Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

A:

Q: 1 2 (24)-- = G ) (2A)-1 3 4

A: (2A)-1 = 1234taking inverse both side :((2A)-1)-1 = 1234-12A =  1234-1Let B = 12342A = B-1A = 12B-1…

Q: Table Q4(b) is generated from the function f(x)= e* – 4x² + B , where B is the last two digits of…

A:

Q: -1 Suppose A, B, C, X are invertible n x n matrices. Solve the matrix equation C(B1X) = (B-²C-1) B²…

A: If A and B are nxn invertiable matrices then(AB)-1=B-1A-1