Given the vector x = (1, 2, 2)T , find a Householder matrix that will zero out the last two entries of x.

Q: find the elelment in the 3rd row and 1st column of the matrix cofactor 7 2 5 3 1 4 1 2 1

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Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

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Q: a) Find the matrix of the quadratic form. Assume x is in R3 5x3-x3 +7x3-5x1x2 -3x1x3

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Q: If Q1 and Q2 are orthogonal matrices, show that their product Q1 Q2 is also an orthogonal matrix.…

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Q: Determine all 2 × 2 matrices A such that AB = B A for any 2 × 2 matrix B.

A: Let A=abcd and B=pqrs be any 2×2 matrices.

Q: and the SUD of the following am A= 11 94040 220

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Q: Find 2 × 2 matrices A and B such that т 6 ]A+[, -1 JA+I 5 -5 ]B = [ 4 -6. ] and -2 -1 4 0 -2 -4 3 -4…

A: Given: The equations  06-1-1A+5-534B=4-60-2T0-211A+-4-8-3-6B=3-47-3T

Q: Show that the matrix equation has no solution.

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Q: Construct a 3 x 3 nonzero matrix A such that the vector 1 is a solution of Ax = 0. 1 A =

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

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Q: 9. Show that the matrix 0 0 -1 0 0 1 -1 C2 = x, x- will transform the vector y into -y

A: We have to show that the matrix C2 will transform the vector in ℝ3 into the vector -x-yz. First we…

Q: O True

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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: Find a 2 x 2 matrix such that 3 -2 -2 = 61

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Q: Find ∣A−1∣ for the matrix

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Q: Suppose column 4 of a 3 by 5 matrix is all zero. Then x4 is certainly a ____ variable. The special…

A: Let A be a 3×5 matrix. Given that column 4 of a matrix A is all zero. We need to find special…

Q: Suppose we are given A E Mmxn(C). How do the singular values of A relate to those of its adjoint, A*…

A: Please check step 2 for the solution.!

Q: Find all matrices B that commute with 1 + i (¹+1) :). 0 A = That is, for which AB = BA.

A: Let B=abcd be the matrix such tghat AB=BA

Q: 1 0 2 -2 3 1 3X +|2 1 3 -1 -2 0 4 -1 5 1 5 II

A: The given equation is,

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: matrix A if (A" – 21)* = } Determine the matrix A if %3D

A: Given,             12AT-2I-1=1234To find : The matrix A.

Q: The matrix X1 X = is called a vector.

A: We have to find

Q: Write down the (3,3) entry of the inverse of the matrix [1 2 3 122 1 1 1 A

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Q: Identify a matrix P that diagonalizes 2 6 A = a. 1 P = - 2 Ob. P = -1 0 0 2 Oc. P = 01 1 2 O d. -2 P…

A: Solution

Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

Q: Let A and B be square matrices of order 3 such that |A-| = x + 7 with x + -7 and |A * A" | = . What…

A: A and B are square matrices. Therefore, det(AB)=det(A).det(B) det(A)=det((A)T) We will use these…

Q: o matrices A and B one has that Null(B) is contained in Null(A · B).

A: Given, for two matrices A and B, to show that Null (B) contained in Null(A·B).

Q: Use the definition of Ax to write the vector equation as a matrix equation -2 + Z2 - 5 3 +Z4 2 4 Z1…

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Q: If A is a positive definite matrix and B is positive semi-definite, show that trace (AB) 2 O with…

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