Let  A be a symmetric tridiagonal matrix (i.e., A is symmetric and aij = 0 when ever |i−j| > 1). Let B be the matrix formed from A by deleting the first two rows and columns. Show that det(A) = a11 det(M11) − a212 det(B)

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A: We can solve this as follows:

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A: Given: 02-135-2-3-51X=-1000-50004 If AX=B, then X= A-1B. We know that A-1=adjAA and adjA= cofaijT

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A: trace is the sum of all diagonal elements of the matrix.

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A: Solve the given problem.

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A: Introduction: It is the sum of the diagonal elements of the matrix from upper left to lower right.…

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A: M=1A-B0-1C002 Now characteristic equation is, M-λI=0⇒1-λA-B0-1-λC002-λ=0⇒1-λ-1-λ2-λ-0=0    By…

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A: Determinant of a null matrix is equal to zero.

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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A: In this question we have to find detA-1.

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A: Given: All the given matrices are n × n. A and B are row equivalent matrices.

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Q: snip

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A: Wee need to find matrix A and B and do their addition and find invertible

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A: A be a nilpotent matrix of order n

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A: We will use the knowledge of standard value decomposition.

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A: First we need to find eigen values: