A lower triangular matrix of matrix A is c. L = Ex Ek1... E, E,. ... Ek1 E, d. L = E, E, a. L = E, E2 ... Ek-1 Ek -1 b. L= E, E1. ,E, E, E,1 ... O B O D

Q: Use a graphing utility with matrix capabilities to find the following, where u = (1, 2, 1, -3), v =…

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Q: Let (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

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Q: Matrix  A = a11 a12 a21 a22 a31 a32 B =  b1 b2 C = c1 c2 c3     Find C*A. Find C*B.

A: The product of matrices is given as follows

Q: What are L and D (the diagonal pivot matrix) for this matrix A? What is U in A = LU and what is the…

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Q: Let B=(b₁,b₂), C={C₁,C₂), be bases for R² b₁ = (-1,2), b₂ = (1, -1), C₁=(1,2), C₂ = (1,1) Find the…

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Q: Put as many 1's as possible in a 4 by 8 reduced echelon matrix R so that the free columns are(a) 2,…

A: In a reduced echelon form of a matrix, if there is a pivot element in a row then, the elements above…

Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

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Q: Use the facts that det(E3E2E1E0A) = 1 and • Eo is a replace matrix (−5A9,: + A7,; → A7,:) E₁ is a…

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Q: Do the columns of the matrix span IR? Select an Answer v 1. 3 3 -3 3 A = -5 -4 3 -1 -4 -4 4 -4…

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Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

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Q: 33-6 -26] A = 33 8. 21 39 -8

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Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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Q: Find an SVD of the indicated matrix. (Enter each matrix in the form [[row 1], [row 2], ...], where…

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Q: Let B be a 500 x 500 matrix. Let A adjoint matrix of B, and M=minor matrix of B. Let Ai,j denote the…

A: The minor matrix is the determinant of the matrix that is formed by deleting the ith row and jth…

Q: -() --()-() 3 6 3 3 1 2 1 2 1 1 2 1 3 1 2 3 2 2 A = 3 1 2 В C = 4 4 3 4 4 3

A: Claim: We have to find E such that EA=Bi.e. E=BA-1 And F such that, FA=C i.e. F=CA-1 A=121312443then…

Q: Diagonalize the matrix 1 0 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix D…

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Q: A = 2 - 4 4 -2 6-9 7 -3 -1 -10 18 -7

A: Sol

Q: Use the matrix P to determine if the matrices A and A' are similar. 13 4 P = - 12²]-[-28-12] - [23]…

A: I have explained everything with in the solution. Please go through that.

Q: Question 2. Write the 4 × 4 matrix of entries [a] with aj %3D i+2j

A: To Find: 4×4 matrix of entries aij with aij=ii+2j. Concept:…

Q: 6. Let A be a 2x 2 matrix such that (a) The above equations can be written in the form A -1 0 -1 0 B…

A: The objective is to find the matrix B. heck whether the matrix B is diagonalizable or not and also…

Q: Let B = {b1,b2} and C = {c1, C2} be R². Produce the change-of-coordinate matrix from B to C and from…

A: The change of basis matrix form B to C (or from the basis B to the basis C ) and C to B where B and…

Q: Let 2 -1 A = 1 -1 0 2 Find an orthogonal matrix P and a diagonal matrix D such thatt D = P"AP. D =…

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Q: Let A, B be two matrices with linearly independent columns. If Col(A) = Col(B) then A(AT A)-1 AT =…

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Q: Use a graphing utility with matrix capabilities to find the following, where u = (1, 2, 1, -3), v =…

A: Given  u = (1,2,1,-3) v = (-2,2,0,-1) w = (-2,3,1,2)

Q: Find the change-of-coordinates matrix from B to the standard basis in R". 2 -2 3 8 -2 7 8. Pa

A: Uf7ygth

Q: To divide the LHS by a matrix on the RHS, what steps do you follow?

A: To find: To divide the LHS by a matrix on the RHS, what steps do you follow?

Q: Find the LDU factorization of -2 -2 6 4 -15 -10 A = -6 3 -13 -14 -2 14 46 35 That is, write A = LDU…

A: Given A=−2−26425−15−10−63−13−14−2−144635. Find the LDU factorization of A.

Q: What is the condition for a diagonal matrix to be orthogonal?

A: use the properties of orhtogonal with respect to a diagonal matrix...

Q: Which of the following statements is (are) true if B is a basis for the vector space V ○ (a) In some…

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Q: Diagonalize the matrix -5 -2 A = 3 [ by writing it as A = PDP-1

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