Problem 3 1. Prove that B (51, b2, b3,-4} {а, ег#3+ега, +6) is the basis for R4. al 2. Find 1 4 0...
Tbi b2 Problem 24 : Let b e R4 be a fixed vector, b+0. b3 b4 Define L:R4 → R by 11 12 L(x) = 6-2, x= ER 23 24 where b.x is the dot product of b and 2 in R4. (a) Show that L is a linear transformation. (b) Find the standard matrix representation of L. (c) Find a basis for and the dimension of Ker L. (d) Is L one-to one? Explain why. (e) Is L onto?...
Problem 24 : Let b b2 b3 ba E R4 be a fixed vector, b + 0. Define L:R4 R by C1 12 L(x) = b. I, 2= ER4. 13 24 where bºx is the dot product of b and x in R4. (a) Show that L is a linear transformation. (b) Find the standard matrix representation of L. (c) Find a basis for and the dimension of Ker L. (d) Is L one-to one? Explain why. (e) Is L...
Find the coordinate vector [x]g of x relative to the given basis B = {51,b2,b3}: 1 2 2 by = -3 b3 = b -1 x= -5 4 5 4 [x] = (Simplify your answers.)
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(4 points) Consider the basis of R5 given by with b2 (2,-1,-5,-4,7), b3-(3, 2,-7,-5,9) b4 2,1,4,4,-5) bs (-1,0,1,2,0) The MATLAB code to produce the basis vectors is given by b1 11,0-2-2.3], b2 -12-1.-5-4,7T, b3 13-2-7-5,91, b4 [-2,14.4-5T, b5 1-1,0,1,20 Let S denote the standard basis for R a Find the transition matrix P P,s PB,s b. Use the previous answer to calculate the coordinate matrix of the vector z ( 1,5, 4, 3, 3) with respect...
Assume that the transition matrix from basis B = {b1, b2, b3} to basis C = {c1, c2, c3} is PC,B = 1/2*[ 0 -1 1 ; -1 1 1 ; 1 0 0 ]. (a) If u = b1 + b2 + 2b3, find [u]C. (b) Calculate PB,C. (c) Suppose that c1 = (1, 2, 3), c2 = (1, 2, 0), c3 = (1, 0, 0) and let S be the standard basis for R 3 . (i) Find...
Let B = {b1,b2, b3} be a basis for a vector space V. Let T be a linear transformation from V to V whose matrix relative to B is [ 1 -1 0 1 [T]B = 2 -2 -1 . 10 -1 -3 1 Find T(-3b1 – b2 - b3) in terms of bı, b2, b3 .
I need all details. Thx
9. Consider a basis B = {bi, b2} of a sulspoo, W of R4 where -3 (a) Determine the coordinates of x(3,-1,-2,1) in the basis B (i.e. fnd x). (b) Suppose that bl el-C2 and b2 2c1 +c2. Determine the coordinates of x = (3.-1,-21) in the basis C = {c,,c) (i.e. find [x le) (e) Suppose t dbb an d2b 3b s D- di da a basis of W Why or why not?
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Problem 4 Let W a subspace of R4 with a set of basis: 1 [01 [2] 0 11 lo lo] Li Find and orthonormal basis for W!
Problem 4 Let W a subspace of R4 with a set of basis: 1 [01 [2] 0 11 lo lo] Li Find and orthonormal basis for W!
Let W Span((2,-3,0, 1), (4,-6,-2, 1), (6,-9,-2,2) R4. (a) Find a basis for W (b) Find a basis for W (c) Find an orthogonal basis for W and W (d) The union of these two orthogonal bases (put the basis for W and W what? Why is the union orthogonal? into one set) is an orthogonal basis for
Let W Span((2,-3,0, 1), (4,-6,-2, 1), (6,-9,-2,2) R4. (a) Find a basis for W (b) Find a basis for W (c) Find...
9. Consider the matrix A = | 1-3 51 (a) Find A-1. (b) Use A-1 to solve the systems Ax = bı, Ax = b2 and Ax = b3, where b = [1]. bx= [] be= []; without using Gauss-Jordan elimination.