Find the inverse of the matrix using elementary matrices a) 2. b) 3. 2. c) 2. d) 1 3. 1.

Q: Prove that if B is the matrix obtained by interchanging the rows of a 2 ×2 matrix A, then det(B) =…

A: Let the matrix A and the new matrix B be as follows.

Q: Let C be an nxn matrix that satisfies C2 -3C–2In 0. Show that C is invertible and C=1 = }(31-A)

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Q: Express the quadratic form (c₁r1 + c₂2+...+Cnn)² in the matrix notation TA, where A is symmetric.

A:

Q: Let E and F be n × n elementary matrices and let C = EF. Is C nonsingular? Explain.

A: Let E and F are elementary matrices and let

Q: Find a matrix B such that AB = I, where 4 1 1 0 A = and I = -4 4 1 a b Hint: Let B c d B =

A:

Q: the matrIX A into a product QDQ" where Q is orthogonal and D is diagonal.

A: Given,          A=-5-1-1-1-3-1-1-1-3

Q: d. Form [T2] and [T1] and compute the matrix products [T2][T1] and [7T1][T2]. Verify that they equal…

A: The solution is given as

Q: Let A and B be nxn inversible matrix. Prove that AB is invertible and (AB)-1=  B-1A-1.

A: Let A and B be n x n invertible matrices, with inverses A-1 and B-1, respectively.

Q: Use the matrix P to show that the matrices A and A′ are similar.

A:

Q: Let A and B be invertible 5-square matrices such that A| = 4 and B = 2. Then |2A. B 2 %3D

A:

Q: For the matrix A in , use the Cayley ­Hamilton Theorem to compute A2, A3, and A4 by expressing each…

A: Given matrix is

Q: Consider A and B are two square matrices and B is a scalar. Calculate (BA^T B)^(-1) = *

A:

Q: Let X Give an example of two 2 × 2 matrices A and B, neither of which is the identy matrix I, such…

A: Ok

Q: - |A°| |B°| • |4°|

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Q: Let A and B be n × n matrices and let x ∈ Rn. How many scalar additions and multiplications are…

A: Let A and B be n × n matrices and let x ∈ Rn

Q: let A nonsingular matrix, c #0, c scalar (cA)" = CA -1 -1 %3D Select one: True O False

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Q: State Cayley-Hamilton theorem and prove this for following matrix [1 1 A 1 2 -1 %3D [5 8

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Q: Determine whether the following matrices are diagonalizable or not. Explain your answer. 1 1. А — […

A: Find eigen values by solving the characteristic equation:B-λI=02-λ202-λ=0λ2-4λ+4=0λ1=2=λ2These are…

Q: Consider the matrices A = [₁, B = 3₁ C= ¹), D=1 K₁ = [5], K₂=[₁²2] Solve AX + BY = K₁ CX + DY = K₂…

A: Concept: We have the matrices A=3211 , B=0110 , C=111-1 , D=11-14 Now the matrices X and Y are…

Q: Let A and B be square matrices of order 2 such that |B| = 4 .What is ( AB) '

A: To see 2nd step

Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R², where [1 C2 7 3 3 b1 b2 3 10 22 b7 what is…

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Q: Use Gauss-Jordan to find the inverse of the matrix A given by -3 0 0 2a b a A = 10 0 2 What are the…

A: Gauss Jordan’s Matrix Inversion method. In this method we shall find the inverse of a matrix…

Q: Find all a,ß>0 so that the matrix 3 2 B [4]= a 5 B 2 1 a is strictly diagonally dominant.

A:

Q: Show that ||AB||F ≤ ||A||2||B||F and ||AB||F ≤ ||A||F||B||2 for all matrices A and B.

A: The Frobenius norm for a square matrix A is defined as AF=∑i,j=1naij212. The Frobenius norm…

Q: State whether the matrix is diagonalizable or not. 0 0 7 0 O diagonalizable O not diagonalizable

A:

Q: Determine whether or not ( ABC )T = C"B"AT for matrices: A, B, C

A: Given- ABCT=CTBTAT To Determine- Whether the above statement is correct or not for matrices A,B,C.…

Q: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 3 -21…

A: Given;                           A=13-223001-1 Start with A I…

Q: Find two 2 × 2 matrices A such that A2 = I.

A:

Q: Find a matrix B such that AB = I, where [ ] 8 1 1 0 A = and I = -8 8 0 1 1 a b Hint: Let B = %3D c d…

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Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1 A =0…

A: Given,

Q: Find nonzero 2 × 2 matrices A and B such that AB = O.

A: Consider

Q: Let A be a 3 x 3 matrix such that 3a(1)- 2a(2)+7a(3)=0. Is A nonsingular? Explain.

A: A is singular matrix if rank is not full

Q: Find two non zero matrices A and B such that AB = 0. %3|

A: Find the two matrix which satisfy the given condition

Q: Fill in the missing entries of Q to make Q an orthogonal matrix

A:

Q: Find the inverse of the matrix A, then prove that Ax A-1 =1, 3 -2 1) A =

A:

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1] A…

A: NOTE:We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, -1] -1…

A: The given matrix is: A=-11-10-1012-2 It is given that, A is a non-singular matrix. It means the…

Q: (b) Compute the inverse matrix of T.

A:

Q: Prove that A+ A' is a symmetric matrix, w

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Q: Generalize the result by proving that, for any comfortable non-singular matrices A,B and C the…

A: Consider the given information. ABC-1=C-1B-1A-1 Multiply by pre and post C.…

Q: b) Consider the matrices C and D: C = D = -8 2 at 8.49.35 AM Calculate matrix 2C + 3D.

A:

Q: Given the cofactor of matrix A, What is the adjoint of A?

A: Adjoint matrix is the transpose of cofactor matrix.

Q: State whether the matrix is diagonalizable or not. [:] 0 7 0 0 O diagonalizable O not diagonalizable

A: Given matrix is 0700 and now subtract λ from the diagonal elements=0-λ700-λThe determinant is…

Q: Consider a matrix A, and let B= rref(A). %3D a. Is ker(A) necessarily equal to ker(B)? Explain. b.…

A: The matrix B=rrefA is the Reduced Roe Echelon form of the matrix A. The kernel of a matrix A is the…

Q: Let A = a) Find all matrices B e M2(C) which commute with A. b) Find all matrices B e M2(C) for…

A: We know that  two matrices X & Y commute if  X Y=Y X We are given matrix A. We have to find all…

Q: Let A, Band C be square matrices Such that AB = AC, If A#0,then B-C. 1s this True or false? Explain…

A: Let A, B, and C be square matrices such that AB=AC. If A≠0 , then B=C. Determine true or false.

Q: Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

A:

Q: Find two 2 × 2 matrices A such that A2 = O.

A: to find a matrix A

Q: Find all a and B> 0 so that the matrix 4 a 28 5 4 2 is strictly diagonally dominant.

A: In a diagonally dominant square matrix, the magnitude of the element corresponding to the diagonal,…