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

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 =

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Q: Find x such that the matrix A is equal to its own inverse.

A: We have A=-2-33x Now, A-1=1AadjA For a 2×2 matrix A=abcd, we have A=ad-bc  , adjA=d-b-ca Hence, for…

Q: Let A be an 4 x 5 matrix and B be a 5 x 3 matrix. Then the product AB and BA are definec True False

A: Let A be an 4×5 matrix and B be a 5×3 matrix. Then the product AB and BA are defined. We have to…

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: Let A be an m×n matrix and let B be an n×p matrix. Show that if the columns of B are linearly​…

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Q: Let a be a real number, and consider the matrix a 2 1 1 6 3 A =

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Q: Let A be square matrix. If A" = 0. A= Oava %3D for n> 2. Then

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Q: nd an invertible 2 x 2 matrix P and a 2 x 2 diagonal matrix D such that P-¹ AP = D, and determine…

A: To solve the following problem on diagonalization given eigen values and eigen vectors.

Q: Show that if A is a square matrix that satisfies the equation A2 -2A +I= 0, then A-1 = 2I -A.

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Q: Find the matrixx such that 2A + B + X =0 where 1 2 3 -2 A = %3D 3 4 1 5 Select one: a. -1 -2 -7 13

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Q: Find three non-trivial 2 x 2 matrices such that the square of the matrix is the zero matrix, i.e: A?

A: We want to find matrix A such that A2 = 0000

Q: Find x such that the matrix is singular. 4-[94] A

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Q: Find a formula in terms of k for the entries of A, where A is the diagonalizable matrix below. 0. A…

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Q: Let If A is 2x2 matrix and /(4)=0, then %3D

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Q: Show that if A is an n x n matrix, then A" can be written as a linear combination of the matrices I,…

A: Cayley-Hamilton Theorem:- Every square matrix satisfies its own characteristic equation.

Q: * Let A be and m x n matrix. Describe the matrix E such that EA is A with row swapped.

A: Given matrix A is a m×n matrix. And the elementary matrix E and EA are row swapped. Since elementary…

Q: Let A be an n × n matrix and let B = A + I. Is it possible for A and B to be similar? Explain.

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Q: Find a 2 x 2 matrix B so that B2 = A, where

A: Given matrix A=-7-16817 To find matrix B such that B2=A.

Q: Decide whether the matrix -7 1 4 A = -12 1 8 -10 1 7, is diagonalizable over R. If it is,…

A: -714-1218-1017

Q: Determine if the matrix A = -1 1 1 is diagonalizable. If so, find P, D, so that -3 -1 -3 DDD-1

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

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Q: Find the two by two matrix A such that A -

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Q: Let A be the matrix a- [}] 3 1 A = Which answer is correct for the A ?

A: GivenA=3121

Q: Find the inverse of the matrix (if it exists). (If an answer does not exist, enter DNE.) 5 11 1 6 15…

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Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: Let A be a 3 x 10 matrix, and let B be m x n. Suppose that B'A' is a 21 x 3 matrix. What is the…

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Q: Let A be an nxn matrix and B = A+1, where I is the identity matrix, then it is possible for A and B…

A: Given A be an n×n matrix nd B=A+I where I is the identity matrix , then it is possible for A and B…

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3 -2]…

A: A=13-223001-1

Q: Let A be a square, invertible matrix and let A' be its transpose. Which of the following statements…

A: Solution

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, A = [6…

A: We have to find the inverse

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: 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: Show that if A is a square matrix that satisfies the equation A2 - 2A + I = O, then A-1 = 2I - A.

A: Given that,                    A2-2A+I=0

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

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Q: If A is a square matrix such that A3 = O, show that (I-A)~l = I + A + A2.

A: To prove that (I-A)~l = I + A + A2 If A is a square matrix such that A3 = O

Q: Find all a > 0 and B>0 so that the matrix 3 2 B A A =| a 5 B 1 is strictly diagonally dominant.

A: The given matrix,A=32βα5β21α

Q: Let A be an n x n matrix and let D be a n x n diagonal matrix. Show that AD =…

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Q: Let A be an n xn matrix and B= A+I, where I is the identity matrix, then it is possible for A and B…

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Q: Let A be an n xn matrix and B= A+1, where I is the identity matrix, then it is possible for A and B…

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Q: Let A be an n × n matrix and c a real number. Show that if cA = O , then c = 0 or A = O .

A: Given: A be an n × n matrix and c be a real number. To prove that: if cA=0 , then c=0 or A=0.

Q: Consider the matrix B given by 0 0 0 B = 1 0 0 0 1 0 Show that B3 = 0. Also, compute for the product…

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Q: Find all a and B >0 so that the matrix B = 23 6 2 is diagonally dominant;

A: A square matrix is diagonally dominant if   for .

Q: Let A be nxn orthogonal matrix and v E R". Then ||Av||? = || ||?. %3D Select one: True O False

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Q: Let A be a 3x3 matrix where A2=I3, then det(A) is 1 or -1. Select one: 1-True 2-False

A: To find- Let A be a 3×3 matrix where A2 = I3, then detA is 1 or -1. True False

Q: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3.…

A: Given :          A = 13-223001-1   To find the inverse of A. Also, to compute 3A-1.

Q: Let A be a 3x3 matrix where A?=13, then det(A) must be equal to 1. Select one: O True O False

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Q: Show that A is similar to B by showing that A and B are similar to the same diagonal matrix, where…

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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,…