Explain the following terms by use of examples: Special matrices Associative law in matrix algebra input output analysis

Q: Find two 3 x 3 matrices A and B such that det(A + B) + det(A) + det(B)

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Q: Let A, B be  matrices of the same order. Then det(A+B)=det(A) + det(B).  True or false

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Q: Write an example of a matrix multiplication that is undefined. If the expression A x B is defined,…

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

Q: factor of the element 4 in the matrix 1 2 3 A = |4 5 6 [7 8 9

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Q: Write the standard matrices of the given linear operators: a) Lị(x) = (x1 + x2, X2 – X1) b) L2(x) =…

A: a) L1(x) = Ax Let A = abcd Then x1+x2x2-x1= abcdx1x2 = ax1+bx2cx1+dx2 On comparing the coefficient,…

Q: 315 241 42-9

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Q: Diagonalize the matrices below, if possible: (a) [1 0 3 2 1 2 0 0 2] (b) [3 1 1 −4 −2 −5 2 2 5]

A: To Diagonalize the given matrices (a)[1   0  32  1   20  0  2]  (b)[3  1   1− 4 −2 −5 2  2  5]

Q: Product of matrices multiplication A=[a, b; c, d] x[1,0;0,1]

A: In the question we have to find the product of the matrix.

Q: 3 X+ 2 5 1 -3 1

A: Solution:

Q: (1) True or False? Justify your answer. (a) Let A, B, and C be two square matrices of the same…

A: for given three matrices with same dimension  and  is invertible,Again as matrix multiplication is…

Q: (A-¹) = (A¹) (assuming A- exists) (AB)−¹ = B¯¹A−¹ (assuming A-¹ and B-¹ exist)

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Q: Let A be a 6 x 6 matrix. Suppose A6 is equal to the zero matrix. Denote by I the identity matrix of…

A: Given A6= 0. We will show all of the eigen values of A are Zero. Then we will show eigen values of…

Q: Define properties of matrix , Explain each of the analogous to a familiar algebraic property of the…

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Q: Does matrix multiplication commute? That is, prove why does it. If not, explain why it does not.

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Q: Classifuy the following matrices: A= 01 01 1l matrices in RREF: DA,B,C,E (b)E,F,H()AB,G0,E 1B,C,E…

A: The correct answer is as follows below:

Q: Show that, the non-zero elements of the inverse of a N*N diagonal matrix is just multiplicative…

A: As per the question,we are asked to prove that the non-zero elements of the inverse of a diagonal…

Q: Verify the following properties of matrix operations: (a) the associative property of matrix…

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Q: 4. 5. Find det(4A). Find the adjoint of A.

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Q: A. The difference in notation between matrix multiplication and tensor multiplication of two tensors…

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Q: If AB + BA is defined, then A and B are square matrices of the same size. True False

A: Given AB + BA is defined.

Q: A square matrix is a necessary condition for which of the following. Choose all that apply: An…

A: A  is identity matrix if all the diagonal entries is 1 and non diagonal entries is zero  Addition of…

Q: Consider the following square matrices. In each case, use elementary row reductions to either: (i)…

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Q: a. Define or explain the process of Inverse of a Matrix (in solving systems of equations). Word…

A: The inverse of the matrix is calculated by a series of steps calculate the determinant of the…

Q: 8. Construct the graph of the following Matrices: Adjacency Matrix 1 2 3 3 4 1 0 1 10 1 2 10 1 1 30…

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