23. If A and B are matrices, then both AB and BA are defined if and only if A and B are square matrices. 24. If A is an m x n matrix and B is an n × p matrix, then (AB)" = A" B" .

Q: all the If matrix D is a 7 x 4 matrix, and the product of matrix D and matrix E, DE, exists, what…

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Q: 31. If A and B are n x n matrices, then the diagonal entries of the product matrix AB are…

A: Matrix multiplication is possible only when the number of columns of first matrix are equal to the…

Q: 4. If det(Adj(A)) = then what is det (A-1) if A is a (4 × 4) matrix?

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Q: If X is an unknown matrix And A and B are known : [A]×[x]=[B]_ 5x5 5×1 [x] = ?

A: Given matrix A is of order 5×5 and matrix B of order 5×1 and A5×5×x=B5×1 We have to find the matrix…

Q: Suppose that A is an n x n matrix such that A² = 0. a) Show that if 7 E im(A), then 7 € null(A). (In…

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Q: 17- Let A be 5 x 5 matrix and det(4) = 2. What is the value of der(24)? a) 128 b) 32 16 64 LEave…

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Q: 3. Show that (AB)* B' A' by using the matrices A and B giver [8 -2 5] 1 -5] B = 7 0 -3 A =1 -4 3 6.…

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Q: Show that if A and B are two n × n matrices with the same diagonalizing matrix X, then AB = BA.

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Q: A is an m x p matrix, B is a p x k matrix, and C is a k x n matrix. Show that A or (B or C) = (A or…

A: Introduction: Matrix multiplication is divided into two types: Scalar Matrix Multiplication, in…

Q: Suppose A is a symmetric nxn matrix and B is any nxm matrix Show that B'AB, B'B, and BB' are…

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Q: Create two 2 x 2 matrices A and B, to show that (A+ B) - A+B is not always true. Clearly write A, B,…

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Q: Let A and B be 6 × 5 matrices. If dimN(A) = 2, what is the rank of A? If the rank of B is 4, what is…

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Q: If for a square matrix A and B. null matrix O. AB = O implies A=O and B=O. True False

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Suppose that A is a 64 × 17 matrix and that the rank of A is 11. What is the dimension of the…

A: The given matrix is A of size 64×17. Also the rank of A is 11. As we know that for any matrix of…

Q: For any two 3 x 3 matrices A and B, we have (А + B)(А — В) — А? — АВ + ВА - В?

A: Given statement: For any two 3×3 matrices A and B, we have

Q: (1) Let A be a px5 matrix, B be amx 4 matrix. If AB is a 7xq matrix, then p= , m=_

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Q: If the null space N(A) of a 5 xX 6 matrix A has dimension 4, what can you say about the dimension of…

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Q: 2 if A=| -3 -2 4 and B= 1 ,find the Matrix X such that 3A+4X=5B 1 3

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Q: (A) IF A 2 ー3 - 6 6 3 -9 and B-4 is (A.B) null matrix.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Suppose that A is a 4 x 4 matrix with det(A) = 5. Then + (24–1) - [2 Enter your answer exactly, as a…

A: We have to find determinant

Q: Let A be an m x n matrix with m>n.  Show that for any n x m matrix B, then AB does not equal Im. Use…

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Q: If A, B, C are square matrices of the same size such that AB = A C, then for sure B = C. True False

A: See the solution below.

Q: 4. Suppose that a matrix A can be writ

A: Given, a matrix A can be written as the matrix product A=BC as follows:…

Q: Let A and B be n × n matrices. If AB = A then B is the identity matrix In. True or False

A: To write that true or false

Q: Suppose that A is an 11 x 4 matrix, and that B is the rref of A. If the number of leading columns of…

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Q: If A is an m x 5 matrix, B is a 6 × q matrix, C is an m × q matrix, and 8A + B - 1/2C is a  6 x 5…

A: Topic:- matrix algebra

Q: 6. Suppose that A is a 3 x 4 matrix. а. Is it possible that dim Nul(A) = 0? b. If dim Nul(A) = 1,…

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Q: If A is a 6 × 8 matrix, what is the smallest possible dimension of Nul A?

A: Consider the provided matrix, Given, A is a 6 x 8 matrix. Since, the rank of A equals the number of…

Q: (5)if A = \4 .B = * are single matrices( is)find x. .4 4

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Q: If B arises from a matrix A by elementary row operations, what is the relationship between NS(A) and…

A: Given matrix B arises from a matrix A by elementary row operation. We have to find the relationship…

Q: If A is the matrix -3 4 3 A 3D 4 3. 1 12 and if 1 u = and V = 3.

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Q: Suppose the matrices P and Q have the same rows as I but in any order. They are "permutation…

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Q: If AT = A-1, where A is a real matrix, then A is

A: When transpose of A equal inverse of A , then A is

Q: 1. Suppose that we have a n × 10 matrix (n rows and 10 columns) where the entries are either 0 or 2.…

A: Just think for different values of n and you will notice that n=2 will work

Q: State, with reason, whether the following statements are true or false. a) If D is a 2x2 matrix with…

A: a) This statement is false, since, we have non-zero matrices with zero determinant. For instance,…

Q: If D is an n × n diagonal matrix, how do the valuesof ||D||1, ||D||2, and ||D||∞ compare? Explain…

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Q: 4. Prove: If A and B are both n x n matrices, then det(AB)= detAdetB. (Only use 2x2 matrices)

A: Given A and B  n×n  matrices to prove  det(AB)=det A det B

Q: O If A is possi ble value of dim Nul AT ? Please explain an 8x 5 matrix, what is

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Q: *3. Suppose A is an n × n matrix and B is an invertible n × n matrix. Simplify the following. a.…

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Q: If A is m x n matrix and Ax b has no %3D solution for some b. then

A: The rank r of a matrix is the number of column (row) pivots, it must be less than equal to m and n.…

Q: 3- If A² [45] [95] 091 (1 find A where A is UPF triangula matrix

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Q: If A and B are nxn matrices such that AB = BA , show that (AB) = A²B² .

A: Suppose A  and  B be n×n matrix  such that AB=BA

Q: If A is a matrix in Rmxn with {()} -5 C(A) = span 2 %3D -2 what is m?

A: If A is a matrix in R^(m×n) then A is a linear transformation form n to m

Q: . We can add (or subtract) two matrices only if they have thesame .

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Q: (A) IF A 2 1 -3 %3D and B= -6 16 3 -9 is (A.B) null matrix. 4

A: I am solving question1  for question 2 repost.

Q: 3. Suppose A is an m x n matrix whose rows are all identical and B is an n x p matrix whose columns…

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Q: Suppose that B is a matrix whose third column is the sum of the first two columns, then the third…

A: We have to solve given problem: Consider B is a matrix whose Ist,IIndand IIIrd column…

Q: 8. If A is an mx n matrix, wh

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If matrix A = then element of a22 of A is: 0 9

A: