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: [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: Q1: For the given matrix A, find (a) The rank of the matrix A, (b) a basis for the row space (c) a…

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Q: By trial and error find real nonzero 2 by 2 matrices such thatA2 = -I BC=O DE= -ED (not allowing DE=…

A: In this question, we have to find real non zero 2 by 2 matrices A, B, C, D and E by trial and error…

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: Factor these two matrices into A = XAX-¹: A 03 X Λ = A: = 3 3 X = Λ 9 9 (Note that you must provide…

A: Step 1: Step 2: Step 3: Step 4:

Q: Find (A, B), ||A||, ||B||, and d(A, B) for the matrices in M2,2 using the inner product (A, B) =…

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

A: Cayley-Hamilton statement

Q: Factor these two matrices into A = XAX-¹: A 03 X Λ = A: = 3 3 X = Λ 9 9 (Note that you must provide…

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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: Let A and B be row equivalent matrices. (a) Show that the dimension of the column space of A equals…

A: Here, A and B are two row equivalent matrices. a) The dimension of the column space of A equals the…

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: Show that any positive definite square root of a diagonal, positive definite 2 x 2 matrix must also…

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Q: Use the inverse matrices to find (AB)', (A')-², and (24)-', -[3}} -2 5 (a) (AB)-1 188 (b) (AT)-1 BS…

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Q: (b) Find a real symmetric matrix C of the quadratic form: Q(x1, x2, x3) = x+ 4x3+ 6x3+ 2x1x2…

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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: Factor these two matrices into A = XAX-¹: A 03 X Λ = A: = 3 3 X = Λ 9 9 (Note that you must provide…

A: Step 1:Step 2:Step 3:Step 4:

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: Find two 3 x 3 matrices A and B such that A · B+ B · A Find a 3 x 3 matrix A that is not the zero…

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

A: Find the two matrix which satisfy the given condition

Q: Make a change of variable, x = Py, that transforms the quadratic form 6x +18x1x2 + 6x2 into a…

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Q: 2 3 10 2 A = 5 4 9 2 3 1 3 multiplying the matrices, explain why A is not invertib

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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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