Let A, B, C, and D be n x n matrices with A invertible. a. Find matrices X and Y to produce the block LU factorization [a })=[{ ЯТЕ B B D and then show that det Ĉ BI= (det A) · det(D – CA-' B) b. Show that if AC = CA, then [¿ 5] det = det(AD – CB) – CB) D

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Q: Let T,(x1,x2) = (+4x1 – 5z2, +1æ1 – lz2), and T2(x1,X2) = (- 321 – 5æ2 , +5æı + 8x2). Write the…

A: To find the standard matrices for T1,T2 and T10T2.

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A: This question is related to Linear Algebra

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A: we have given A and B are orthogonal matrices.  We have to show that the following

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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

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A: here we must know that  1)  AA-1=A-1A =I2) ATT=A3) AI =IA =A

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Q: Let A, B, C be invertible matrices of order 3x3. Show that if AB = AC , then B =C. %3D

A: Let A, B, C be invertible matrices of order 3×3. To show that if AB=AC, then B=C.

Q: Suppose AB = C, where A and C are upper triangular. (a) Find 2 × 2 nonzero matrices A, B, C, where B…

A: Answer

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Q: 1. For any 3x3 matrices A & B: Verify that (AB)" = B"A". %3D

A: By using the properties

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A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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A: Let's find.

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A: A square matrix is diagonally dominant if   for .

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A: We will construct A and put b as a linear combination of column vectors in A.

Q: 2. Find the matrices P and D for an orthogonal diagonalization A=PDPT for 3 0 0 A=

A: First find eigenvalues eigenvactors corresponding to eigenvalues then we get matrices P and D.

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A: Given- A and B are n×n orthogonal matrices. To find- A+B is orthogonal or not?     Concept Used-…