Let X and B be matrices. If we have that B is a symmetric matrix (B is equal to its transposed matrix) and, in addition, it is satisfied that (X' + 22B) BX = 3B, then the matrix X is given by: a) -19(B- T "B. , provided that B I is a non- singular matrix (is invertible) b) -19(T- B) 'B provided that I-B is a non singular matrix (is invertible) c) - 19B(T B) provided that I-B is a non-singular matrix (is invertible) provided that B-I is a non-singular matrix (is invertible) -1 d) -19B(B-I)

Q: Let A be a 5 x 5 matrix with det(A) = -10. 1. If the matrix B is obtained from A by adding 4 times…

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Q: 2. Write the following in vector/matrix notation, specifying all components of the matrices. If it…

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Q: Suppose that A (A, then det(B)- Select one: A. 15 OB. 5. OC -15 ODO th ) is a (4 x 4) matrix, where…

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

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Q: Let A be a 3 x 6 matrix that is row-equivalent to a matrix of the form [I|B], where I is the 3 x 3…

A: We have to find X is invertible or not

Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

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A: To find: dimcol(A)⊥ Given information: A is 8×4 matrix such that rank(A)=3. Concept used:…

Q: If A is an m x n matrix then A' A and A have the same rank. true false

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Q: True False

A: First Part: For the given matrix A, Order=4Rank=3 Note that the rank represents the number of…

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A: Let A be an n×n matrix. we have to give 3 equivalent condition for A to be invertible. Conditions…

Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

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Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

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Q: If A=XDX−1 where  X is a diagonalizing matrix of A, then 7X is also a diagonalizing matrix of A.…

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Q: Suppose A is a 2 x 2 matrix such that A and 1 A What is A-1?

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

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

Q: For which value of x is the following matrix not invertible: 1 1 2x A = 1 2x 2x 2x 2x 2x 4 1 -1 1 2

A: For a matrix A to not be invertible: dat(A) = 0.

Q: If A is a triangular matrix, when is R = rref(A) equal to I?

A: We write the row reduced echelon form of a matrix A as rrefA. A square matrix is said to be an…

Q: Let A be a 3 x 10 matrix, and let B be m x n. Suppose that B'A' is a 21 x 3 matrix. What is the…

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A: Given A = 11-2110B = 11-1111C = 1232-11D = 1-1-9-141

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Q: o matrices A and B one has that Null(B) is contained in Null(A · B).

A: Given, for two matrices A and B, to show that Null (B) contained in Null(A·B).

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Q: [1 3 B = 2 1 5 0 A = 0 -5 4 and 3 8 QA + B'.

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Q: a) Suppose that A and B are 4 x 4 matrices, det(A) = 2 and det((3ATB)-¹) = . Calculate det(B). b)…

A: As per our company guideline we are supposed to answer only one question kindly post remaining…

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

Q: 6. 1 4 If w = -3 E span 2 then x = 1 4 3 Select one: True 21 False

A: As per guidelines, we will solve only first question. Kindly repost other question separately.