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: 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: Let A = 2 1 54 Write 5A. Is det(5A) equal to 5det(A)? 5A= (Type an integer or decimal for each…

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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: solve each of the following for the indicated variable. I = (100M) / C for C (Intelligence quotient)

A: We have to solve the given equation for the indicated variable.

Q: Prove that (a) C(B) C Nul(A), where C(B) denotes the column space of B. (b) rank A + rank B < 5

A: Given that A is a 3×5 matrix and B is a 5×6 matrix. Also AB=0.

Q: If Y and Y are the first and last column vectors in the inverse of a [1 -1 2] matrix A = 0 3 2 then…

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Q: Suppose A is a 8x4 matrix such that rank(A) = 3. Find dim(col(A)-). dim(col(A)+) =

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: Let A be an invertible 3 by 3 matrix. Assume that PA²P-15ATA². = Then det(A) =

A: Step 1:   Step 2: Step 3: Step 4:

Q: We call g(x1, x₂) = ax² + 2bx1x2 + cx a quadratic form, a, b, c are constants. Suppose X1 X = try to…

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Q: Let A, B and C be invertible, nxn matrices with AB BA and I, the n x n identity matrix. If AXB-= I+…

A: Invertible Matrix: An invertible matrix is a matrix for which matrix inversion operation exists,…

Q: SKIP The 4 x 4 matrix A satisfies the matrix equation A = 3A". Find all possible values for det A.…

A: We will use the following properties : (1) det(AT) = det(A) (2) det(AB) = det(A) det(B) (3) det(c•A)…

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

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Q: 6. Find the distance between the matrices A and B, p(A, B), using the ||- ||2 for the matrix -[:] -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: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: If A is a square matrix whose diagonal entries are all zero, then detA = 0.

A: Given information: A is a square matrix whose diagonal entries are all zero.

Q: n 2. Check whether the matrix A- 2 Check whether the matrix A (0 is Hestnitian and Unitary matrix or…

A: The detailed solution is given below Thank you

Q: Let A and C be n×n matrices such that ​CA=I​ (the n×n identity​ matrix). Show that Ax​=0 has only…

A: Here, CA=I, where I is the identity matrix.

Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

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Q: 2. Find a real 2 × 2 matrix A (other than A =I) such that Aº = I . %3D

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Q: Let z be a real number and let A be the matrix 2 I A - (-34). -2 i. Find all values of r such that A…

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Q: Properties of Transpose If r is a scalar and A and B are matrices of the appropriate sizes, then 1.…

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

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Q: Find a 3 x 3 matrix A such that A A A A = 1 4 0 = 2 0 -1 B-B EL. 0 2 1 = -3 and 0 -5 0 -5 B-B 0 -5 1…

A: I am going to solve the problem by using some simple calculus to get the required result of the…