(c) For the real symmetric matrix A, find a non-singular matrix P such that PTAP is diagonal and also find its rank, index and signature where 1-3 2 -3 7-5 2-5 8

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Q: Express the quadratic form (c₁r1 + c₂2+...+Cnn)² in the matrix notation TA, where A is symmetric.

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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: Express the quadratic form (c₁x₁ + C₂X₂ + ... + Сnn)² in the matrix notation TA, where A is…

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Q: Find a matrix X that solves the equation 1 2 3 4

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Q: 9. A = -2 2

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Q: om: A is a matrix such that A2 + 5A 10. Show that A is invertible and A-1 = A + 51.

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Q: 2 3 4 Let vi = 1 V2 = -2 V3 = 5, and E u = V2 3 Determine if u is in Col E, the column space of E.…

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Q: a- B-2 3] and Given matrices Find CAB 3

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Q: (1 b) Write a common matrix with a format (5 x2) form, provide a specific numerical example. Write a…

A: For the solution follow the next step.

Q: Determine the real number values of the constant a with which the matrix A= (14 a1)  is positive…

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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: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

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Q: ebra to show that for n x n matrices A,B,C and n x 1 vector rtible and ABC then the matrix equation…

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Q: Find the power of A for the matrixA16

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Q: for a matrix A 3 6 2 5 if f(x)=(x+2)(x-2), calculate f(A)

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Q: Consider the matrix: 1 2 -2 0 -1 3 4 1-1, Perform R3 - 2R2: 1 2 0 0 3 2 4 3

A: Given query is to perform the indicated matrix operation.

Q: f (x1,X2,x3) = xỉ + 3x1x2 – x2X3 +x3 – 4x3 Rewrite f in the matrix form x'Ax where A is a symmetric…

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Q: Find all real numbers a, b for which the matrix A nalizable in R. = ( 1] is diago-

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Q: Provide the symmetric matrix that generates the following quadratic form Q(x): x+2x+3x3 + x₁x2 - 2X1…

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Q: For matrix A = (4 6 3 5 ). If f(x) = x2 - 5, calculate f(A)?

A: The given matrix is, A=4635. The function is f(x)=x2-5. For matrix multiplication: The number of…