(i) Use the definition of inverse to prove the following: if A and B are n × n nonsingular matrices, then (AB) = B'A!. |(ii) If A, B, and C are all n × n nonsingular matrices, find (ABC) ' in terms of A', B"', and C` '.

Q: Explain the fact “Cofactors are useful when matrices have many zeros”.

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Q: 2. Assume that all the operations are properly defined, solve the following equation for the unknown…

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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: -1 find its inverse A¬'. Check that your inverse is actual in 2 For a matrix A = -3 Ichow vour work…

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Q: a) For invertible matrices A, BE R™×", show that ((AB)")-1 = (A-1)" (B1)". b) Let A, B, C, D e R"*"…

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Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

Q: Consider the matrix in the image (i) Determine the inverse matrix B^−1 , of B. (ii) Using the…

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Q: How do we add and subtract matrices and when are these operations defined?

A: Addition and subtraction of matrices If A=[aij] and B=[bij] are two matrices of the same order, say…

Q: Find the matrices of the two similarities taking (0, 0, 1) to (-2, 4, 1) and taking (1, 0, 1) to (0,…

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Q: Can you please help with finding an inverse of an elementary matrices?

A: An elementary matrix is a kind of matrices that differ from the identity matrix from a single…

Q: Define Matrix Inverse?

A: The inverse of matrix A with order 2×2 can be obtained by elementary row operation on a new 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: If xER" is a column vector (i.e. an n ×1 matrix), then In-2xx' is always a symmetric matrix. True…

A: Consider the given column matrix as x=x1x2⋮⋮xn-1xn, x∈Rn. Compute the transpose of the matrix x as…

Q: = [2 1 3 -1 -1 -1 2

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Q: a) Let A and B be two regular (nonsingular) (n, n)-matrices. Determine whether the following is…

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Q: If A + 0 and B+ 0 are square matrices of the same order, then AB + 0.

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Q: Find the inverse matrix where A = 1 -1 2 -3 -3 1 2 -3 -3

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Q: IA - (34) and B- (-5 8 -2 (a) (AB) (b) BTAT 10. f -5 find

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Q: If A and C are non-singular matrices, then show that A 0 A-1 C-BA-1 C1 1 0 0 0 0 2 0 0 3 0 4 0 1 0 3…

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Q: Let I be the 2 x 2 identity matrix. What is det (-41)?

A: The given data is:  I be the 2×2 identity matrix  To find det-4I Given:  I be the 2×2 I=1001

Q: Use elementary matrices to find the inverse of

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Q: Factor these two matrices into A = XAX-¹: 4 = 3 A [

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Q: Explain why det (BPB¯¹) = det(P) for any matrices P and B. Assume both sides of the equation are…

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