2. The following are ordered) bases for a subspace S of R3. (a) (8 pts. Find...
6. Find a basis for the subspace of R3 spanned by S (42,30,54), (14,10, 18),(7,5,6)). 7. Given that [xlg [4,5,3]', the coordinate matrix of x relative to a (nonstandard) basis B((,1,0(1,0,1),(0,0,0)). Find the coordinate vector of x relative to the standard basis in R3 8. Find the coordinate matrix of x=(-3,28,6) in Rs relative to the basis B=((3,8,0),(5,0,11),( 1,5,7), 9. Find the transition matrix from B ((1,7),(-2, -2))to B'- ((-28,0),(-4,4)) 10 Perform a rotation of axes to eliminate the xy-term,...
2 question ---------------------------------------------------------- (1 point) Consider the ordered bases B =( (8-4] [: • and c- (- -)( :} ) for the vector space V of lower triangular 2 x 2 matrices with zero trace. a. Find the transition matrix from C to B. TB = b. Find the coordinates of Min the ordered basis B if the coordinate vector of Min C is [Mc= [MB = C. Find M. M= (1 point) Consider the ordered bases B [ 1...
Find a basis for the subspace of R3 spanned by S. S = {(4, 4, 9), (1, 1, 3), (1, 1, 1)} STEP 1: Find the reduced row-echelon form of the matrix whose rows are the vectors in S. 1 0 0 1 0 0 0 x STEP 2: Determine a basis that spans S. 35E
Problem 2: Consider the following 2-dimensional linear subspace of R3: X = {(a,b,c) ER’: a+b+c=0}. Define a linear map F: X X by setting F(a,b,c) = (20 – 3b+c, -3a + 2b+c, a +b – 2c). (a) Find the matrix A representing F with respect to the basis 21 = (1,0, -1), 22 = (0,1, -1). (b) Find the matrix A representing F with respect to the basis î1 = (3,1,-4), f2 = (1, -2,1). (c) Find an invertible matrix...
(1 point) Consider the ordered bases B = {-(7 + 3x), –(2+ x)} and C = {2,3 + x} for the vector space P2. a. Find the transition matrix from C to the standard ordered basis E = {1,x}. TE = b. Find the transition matrix from B to E. Te = c. Find the transition matrix from E to B. 100 TB = d. Find the transition matrix from C to B. TB = 11. !!! e. Find the...
solve the linear algebra question 1. (6 points) Let S be a subspace of R3 spanned by the columns of the matrix [1 2 0 1 1] 2 4 1 1 0 3 6 1 2 1 Find a basis of S. What is the dimension of S?
21 and s2- be ordered bases for IR2. Give the change-of-basis matrix from T to 2. Show your work.
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
2) Let B = {(1, 3, 4), (2,-5,2), (-4,2-6)) and B/-(( 1, 2,-2), (4, 1,-4), (-2, 5, 8)) be 5 ordered bases of R2. Let x = | 8 | in the standard basis of R2. a) Use a matrix and x to find L18 ]B. b) Use a matrix and [X]B to find [x)B/. c) Use a matrix and [X]B/ to find x in the standard basis of R2, d) Draw a diagram of the steps a), b), and...
no calculator please 1 (8 pts) Find the dimension and a basis for the following vector spaces. (a) (4 pts) The vector space of all symmetric 2 x 2 matrices (which is a subspace of M22). (b) (4 pts) All vectors of the form (a, b, 2a + 3b) (which is a subspace of R®). 2. (12 pts) Given the matrix in a R R-E form: 1000 3 0110-2 00011 0 0 0 0 0 (a) (6 pts) Find rank(A)...