Let M € M₂ (F), A € M₂(F), C = M(F) and B € Mpxk (F) with n=p+k. Also let O denote the kx p zero matrix. (a) If M show that det (M) = det(A). A B O Ik

Q: 2. Let A be a square matrix with real or complex entries. Show that if A is normal and upper…

A: Definition of normal matrix:

Q: Let A be an invertible matrix. Show that det (adj (A)) = det (A-¹).

A:

Q: For which values of the constants b and c is the follow- ing matrix invertible? 1 b -1 -b

A: The given matrix is 01b-10c-b-c0

Q: Let A = - 2     1    0                 1     0    1                2    -3    1        A is a…

A: trace is the sum of all diagonal elements of the matrix.

Q: Let A be a real 2 x 2 matrix satisfying A? - 4A = 0, where O is the zero matrix. SKIP Find the…

A:

Q: Let A be any invertible 9 x 9 matrix. Which of the following is equal to det(Adj A)? OA. (det A) B.…

A: Given: A is an invertible matrix of order 9×9 We are required to find: det(AdjA)

Q: Let A be a matrix whose entries are integers, and det A=1. 4 : Show that the entries of A-1 are all…

A: given ,det A = 1

Q: Let A = [ 9-8 4-3 Find an invertible matrix X such that X-¹AX is diagonal.

A: Introduction: A matrix A of dimension n x n is called invertible if and only if there exists…

Q: Let (A-2)-1- where / is the identity matrix,then A= Select one: a. 0 3 7 3 2 2 3 3 REDMI NOTE 8 PRO…

A: Explanation of the answer is as follows

Q: Let A = [5 0 X = 5 Find an invertible matrix X and a diagonal matrix D such that X-¹AX = D. 001 D =…

A:

Q: 5. Let D be a non-singular matrix such that 7. (7D)- 1 -2 Find D.

A: Inverse matrices

Q: Let A be a n x n real matrix. If the rank A =n find the following: (a) Col A (b) Nul A (c) nullity A

A:

Q: Suppose A is a matrix. Let B be given by switching two of the rows of A. What is the relation…

A: Switching two rows of a matrix is equivalent to multiplying the matrix by a permutation matrix that…

Q: Let A be an m × n matrix. Under what circumstances will ||A||2 = ||A||F?

A:

Q: ............. 05 Let A = diagonalizable matrix( A = XDX-1), then X and D are: Select one: а. -5 0 1…

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Q: Suppose A is a symmetric matrix. (Au)" : u"A

A:

Q: For which value of x is the following matrix not invertible: 1 1 2x A = 1 2x 2x 2x 2x 2x 4 1 -1 1 2

A: For a matrix A to not be invertible: dat(A) = 0.

Q: Find a matrix X such that AX=B 0 6 A = [²2 -B = [1 2 ] 91 L7 8. 4

A: Given that we have to find a matrix  .Obviously order of the matrix  is .Let Now so  ,

Q: Let A, B, C be nxn matrices. If B = CAC- show that det(A) = det(B).

A: Given that A,B,C be n×n matrices. Also  B=CAC-1 To Prove: det(A)=det(B) To prove the result we…

Q: Find matrices P, D and P-1 that diagonalize matrix A, where A = P = D= P-1 20 0 -11 -2 -3 -30 -1

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Q: Let A be a square matrix such that A = 0. Show that 4 : (I – A)-1 = I+ A+ A? + A³. Here I is the…

A:

Q: If A is square matrix of order 3 such that|3 A| = 54. Find |A|

A: Using the properties of determinants

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

A:

Q: Let A E Rx and B E Rmxm and assume that dim N(A) = k and dim N(B) = l. Let C be an 2 x 2 block…

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Q: Q5. Suppose B = QRQ-1, where Q is orthogonal, and R is upper triangular. Show that if B is…

A:

Q: Suppose A is an n×n invertible matrix such that A – 2A = I, . Find an for A. expression

A:

Q: Let A be the n×n matrix whose only non zero elements are ai+1 i =1, i =1,2,...,n−1. Determine eAt.

A:

Q: A is a reversible matrix of nXn. Show that |adjA|=|A|r1

A: As we know that the inverse of a matrix A is : A-1=adj(A)|A|