Find the examples that satisfy the statement in the given items and show some work how they are correct examples. (a) A 4 × 4 matrices A that is not digonalizable. (b) Two matrices A and B that have the same characteristic polynomial but are not similar. (c) Two diagonal matrices D1 and D2 that are similar but they are not equal.

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

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Q: Determine all 2 × 2 matrices A such that AB = B A for any 2 × 2 matrix B.

A: Let A=abcd and B=pqrs be any 2×2 matrices.

Q: Verify by direct multiplication that the given matrices are inverses of one another. 4 -7 4 2 7 -1

A: GIVEN : A = 1427            A-1 = -7   42-1

Q: Determine whether or not the matrices [5 -3 [5 -1 2 -1 and |4 1 -2 are similar. 3 |2 -1 2 Choose

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Q: For this exercise assume that the matrices are all nxn. The statement in this exercise is an…

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Q: Consider square matrices A & B where A#0, B#0,AB=0. Show that |A|=0 or |B|=0.

A: A matrix is a mathematical object containing numbers arranged in rows and columns. The order of a…

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

A: Cayley-Hamilton statement

Q: しt A and B be similar inrertiblo matricen Ghow that and B" are rimilar

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Q: Let A and B be n x n invertible matrices. Use matrix algebra to simplify A(A¯¹ + B¯¹)B.

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Q: Consider A = 112 0 1 2 (a) Find A-¹ by using row operations on [A1]. List the one you use in order.…

A: Given That : Matrix A=123112012 To Find : 1) A-1 using row operation 2) A-1 using row operation 3)…

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: If ri is a first row of a square matrix A and r3 is the third row of A such that ri = 2(r3) then |A|…

A: By applying elementry row operation we can find the value of |A|

Q: Is the following matrix diagonalizable¹? 3 B=0 0 -3 1] 3 1 0 3

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Q: A square matrix is a necessary condition for which of the following. Choose all that apply: An…

A: A  is identity matrix if all the diagonal entries is 1 and non diagonal entries is zero  Addition of…

Q: 2 B= [11] 3 -1 Write B and B-¹ as products of elementary matrices.

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Q: = [2 1 3 -1 -1 -1 2

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Q: Determine if the following matrix is in reduced form. If not, indicate the row operation(s)…

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Q: Use elementary matrices to find the inverse of

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Q: A B 0 D where A, B, D are 2 x 2 matrices and 0 is the 2 × 2 zero matrix. Prove that det(M) det (A)…

A: Given : M=AB0D  where A, B , D are 2×2matrices and 0 is the 2×2 zero matrix. To prove : det(M) =…

Q: Show that is A is a square matrix, then A + AT is a symmetric matrix. You can use any matrix for A…

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Q: Given the matrices [A] and [B], when performing the operation [A] [B] = [C], shows the…

A: [A] is 3x4 and [B] is 4x5. So, [C]=[A] x [B] is 3x5.   So, C42 does not exist.