Working over R: (a) is it possible to find distinct 2 x 2 matrices A, B which are similar but not congruent? (b) is it possible to find distinct 2 x 2 matrices A, B which are congruent but not similar?

Q: Determine which of the following identities are true for all 2x2 matrices A, B, C. (Select all that…

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Q: [5] Find three different 2 by 2 matrices that have A₁ = A₂ = 0.

A: Three different 2×2 matrices that have λ1=λ2=0 i.e, both eigen values are 0 are 0100,0020 and -4-284

Q: Working over R: (a) is it possible to find distinct 2 x 2 matrices A, B which are similar but not…

A: The objective of this question is to understand the concepts of similarity and congruence in the…

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

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Q: For a matrix A: -101 0 0 0 10-1 Find the orthogonal complement of Im (TA)

A: Orthogonal complement of the space

Q: 1 -27 Given: A1 -2 5 2 1 a. Find the inverse of A using elementary row operations (label properly…

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Q: Suppose that  |A| + |B| = |A + B| , find a 2x2 matrix for A and B

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Q: 6 0 -1 -3 23*2 4 -3.0 2 4 -5 -13х2

A: As per the question we are given an expression consisting of two 3×2 matrices and their linear…

Q: Let A and B be 3 × 3 matrices such that det (B) = -2 and 27 = det (-3AB A" B ²). 2 Find det(A).…

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Q: True or False: For n × n matrices A and B, define A ⊗ B = AB − BA. The operator ⊗ is not…

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Q: O True

A: True

Q: () Write the statement of Cayley-Hamilton theorem for square matrices.

A: Cayley-Hamilton statement

Q: Let V = [- 7, – 7,0] and V½ = [0, 3, – 4]. Use the Gram- | Schmidt procedure to construct an ordered…

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Q: (18) Does a 2 × 2 diagonal matrix commute with every other 2 × 2 matrix?

A: We have to check

Q: Let A.3 be 5x5 matrices such that det (A) = 7 and det(A)=-3. Find the following (1) det(2(A^B)')…

A: if A is an n×n matrix and det(A)=a thendet(kA)=kn×adet(A-1)=1adet(AT)=adet(adj A)=an-1

Q: ) Let A, B be matrices with real coefficients. (a) Find A and B such that AB is defined and BA is…

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Q: Given two matrices A and B, how can you determine the order of AB, assuming that the product is…

A: Let order of A is mxnAnd let order of B is nxp (because product of AB is defined)

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: For n × n matrices A and B , when does (A + B )(A − B ) = A 2 − B 2?

A: Commutative rule: The product of two matrix does not follow commutative rule: AB≠BA Given:…

Q: If then which of the following are true? Select one: O det -2c 3 f -h -i -2a-2b 3d 3e [3a -b 2c det…

A: Given :        abcdefghi=3  If each element of a row (or a column) of a determinant is multiplied by…

Q: [2 2 Give two different matrices B so that in each case B 2 2

A: Given matrix

Q: Show that A satisfying A P-¹BP. P-1 -4 2 0-21 0-2 and B (-4(2sqr (-2i(2sqr (-2i(sqrt( 2i(4sqrt(…

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Q: Explain if the statement is true or false, and why

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Q: 1. (a) Consider the matrices A = 2 3] 5 789 [1 4 6 and B = 21 0 without finding the product AB, find…

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Q: TRUE or FALSE: Determine whether the following statement is true or false and explain your answer.…

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Q: (b) For matrices A = compute following (i) AB and BA -1 -2 1 " B = [ 3² 3], 0 = [-2² 1²/2 41-²-3 and…

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Q: Determine: 1 [1 -1 2] [2 3] +|0 1 -1

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