Q2: (a) For given matrix A, find a 3 x 3 non-singular matrix P such that p-1AP is diagonal. A = |-3 -5 -3 3 3 1 (b) Find A10 for matrix in part (a).

Q: Find the matrix of the quadratic form 2x,² + 3x2² – x3² – 4x1x2 +2 x1X3 + 6x2X3

A: The symmetric matrix for quadratic form ax12+bx22+cx32+dx1x2+ex2x3+fx1x3 can be written as…

Q: Give an example of a 4 x 4 matrix that is symmetric, has with the (2,4)-entry equal to -5, and has…

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

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Q: If A is 4x4 matrix with det(A)=10, find det (24-¹A), det (A²).

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Q: Find (a) the nullspace, (b) the nullity, and (c) the rank of the matrix A. Then verify that rank(A)…

A: It is given that,  A = 10-204-24-2-2013. a) Find the null space of A. b) Find the nullity of A. c)…

Q: Q2. For the matrix, A = (a) Find 2 Tr (2 A). (b) If A = 21 8 7 4 6 7 5 4 find (A)-².

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Q: Ei) dim(COLA) is (ii) dim(ColA)- is (ii) dim(RowA) is (iv) dim(RowA)- is (v) dim(NulA) is

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Q: Table Q4(b) is generated from the function f(x)=e* – 4x² + B , where B is the last two digits of…

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Q: Let A be a 3 x 5 matrix in which not all entries are zero. (a) What size must the matrix B be for AB…

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Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Q1. (b) Determine whether the statement is true or false, and justify your answer. (a) The product…

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Q: -3 -1 Find all a so that the matrix A = 1 -1 is positive -1 4

A: Matrix A is position if and only if all of the leading principal minors are positive.    Then follow…

Q: Q(x1,X2, x3) = 2xỉ + 3x3 – x + 5x1x3 + X2X3

A: Given,        Q(x1, x2, x3)=2x12+3x22-x32+5x1x3+x2x3

Q: (b) Table Q4(b) is generated from the function ƒ(x)= e* - 4x² + B , where B is the last two digits…

A: Given: fx=ex-4x2+B To find: f'1.5

Q: 2 -1 3 1 0 0 1 A = -1 2 no

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Q: , and c

A: Given quadratic form is, Here, A is symmetric matrix as,

Q: (b) Find a real symmetric matrix C of the quadratic form: Q(x1, x2, x3) = x+ 4x3+ 6x3+ 2x1x2…

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Q: If A is a 3 x3 matrix and det(A) =-3, what is det(4A)?

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

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Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: Solve A x A T matrix: A = -2  1  -1 3   -3   2

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Q: Find a 2 x 2 matrix such that [3]==1] (incorrect) 4 -2 -2 Answer(s) submitted: C

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

A: Given: Matrix A=3625 To Find: f(A) when f(x)=(x+2)(x-2)

Q: If A is n x n matrix, invertible, and B is n × n. Then Col(BA) =Col(B) O True O False

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Q: If matrix [A] is a 5x5 matrix and a matrix [Z] is obtained by the row operations of replacing Rowl…

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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…