Answer (c), and (d) only. Exercise 4.7 Consider, for varying a € R, the matrix: 01 a 1 0 2 2 2 a +1 Aa = a) Establish if the subspace ((1,0,0), (0, 1,0)) contains eigenvectors for Aa. b) Determine the eigenspaces of Aa. c) Say for which a € R the matrix is diagonalisable. d) For a 0, determine a matrix H such that H-¹AH is upper triangular.

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

A:

Q: let Amxn matrix , c scalar If cA=0, then Select one: a. c=0 and A=0 b. c=0 or A=0 C. C0 or A=0

A: WE have to check the meaning of cA=0.

Q: Let y= and u= 3 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.

A: Describe y as the sum of vertices x1 in span u and x2 orthogonal to u         x1=α9, 3=9α, 3α and…

Q: Let Q be the n × n real matrix in which each entry is 1. Show that det(Q−nIn ) = 0.

A: Given:         Q=11....111....1....................11....1n×n,…

Q: Prove that (A + B)² = -(A + B) in matrix..

A:

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

A:

Q: [1 -1 2 12 Let A : -1. Find the matrix B such that (B + I3)-1 = A.

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Find the change-of-coordinates matrix from Bto the standard basis in Rn.

A:

Q: Let A be an m × n matrix and r, s E R two scalars. Show the property that (r + s)A = rA + sA.

A:

Q: 10. B =

A:

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

A: We have to find all real numbers  for which the matrix  is diagonalizable in

Q: Q4 let V=M₂x₂ of the form [a of with standard matrix addition and multiplication form -space-

A:

Q: Exercise 5H. Let X be a square matrix with real entries such that XTX = I. Argue that det(X) = +1.

A: Clearly X is orthogonal matrix . And the determinant of orthogonal matrix is 1,-1

Q: Let A be an m x n matrix, v be a vector in R", and c be a scalar. Show that A(cv) = c(Av).

A:

Q: Let y= Write y as the sum of two orthogonal vectors, one in Span (u) and one orthogonal to u. and u=…

A: