2. A nilpotent matrix is a square matrix A € Mnxn (F) such that Ak = 0, for some integer k. -3 1 0 2 3 -1 (b) Prove that every nilpotent matrix is not invertible. (a) Show that the matrix B = 1 2 - is nilpotent.

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A: We have to write in the linear combination.

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A: According to the given matrix A, find an invertible matrix P such that .

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A: ANSWER :

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A: We have to solve given problem:

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A: Given that  A is an n×n matrix and c is a scalar. Check whether detcA=cdetA is true or false.

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Q: 1(a) Two 3x3 matrices A, B satisfy the relation: A BA=6A+BA. Given: [1/3 A = 1/4 1/7 Find matrix B.…

A: Here we have det (A^-1) = 1/84. So A is invertible and A^-1 exists. Now A^-1*B*A = 6*A + B*A    Or,…

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A: Q.4

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Q: 1 4 [-1 Form the Matrix Ak? 3.Let Matrix A = 2 3 and k be any scalar b = -4. -3]

A: We need to find Ak.

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Q: -1 [A] = 4 3 -3 2 %3D L3 1] 2.

A: Given :                    2-134-32321 To find :                 The cofactors for C13 , C22 , C32…

Q: (e) Suppose we just had the matrix A, but not the expression that was used to generate it. He we…

A: Suppose we just had the matrix A but not the expression that was used to generate it.

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