We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Problem #9: [2 marks] Let W be the the subspace of M14.14 (i.e., 14 x 14...
slove fast plz
6) [15 marks] Let V be the vector space of all 2x2 matrices over R. Let W, be the subspace consisting of matrices A such that , + Ay = 0, and W, be the subspace consisting of all matrices B such that B2+ Bx = 0. i. [5 marks] Find a basis for W; ii. (5 marks] Find a basis for W,; iii. [5 marks] Find dimW,, dimW,, dim(W+W,) and dim(W, nw).
-9 2. Let Vi-8.V2,andvs-2, let B -(V,V2,Vs), and let W be the subspace spanned , let B -(Vi,V2,V3), and let W be the subspace spanned by B. Note that B is an orthogonal set. 17 a. 1 point] Find the coordinates of uwith respect to B, without inverting any matrices or L-2 solving any systems of linear equations. 35 16 25 b. 1 point Find the orthogonal projection of to W, without inverting any matrices or solving any systems of...
3. Let V be the subspace of M2x2(R) consisting of all matrices in which the sum of entries on each row is equal to 0. Let W be the subspace of M2x2(R) consisting of all matrices in which the sum of entries on each column is equal to 0. Find a basis of V +W.
d. Let W, - W, n W,. Find a basis for W, (but don't prove it). What is the dimension of w? ld J matrices. the subspace of symmetric 3x3 W, A in M: A" -A : Ws = the subspace of 3x3 matrices having the property that the sum of its entries is zero
d. Let W, - W, n W,. Find a basis for W, (but don't prove it). What is the dimension of w? ld J
matrices....
Problem 5 Let W-(a an z Show that W is a subspace of R. + za} e R4 | a5= 22 - Determine a bansis for W, and find its dimension (asa vector space over R)
4. Consider R2x2 with inner product (A, B) tr(ATB), and let V CR2x2 be the subspace 1 1 1 0 This is consisting of upper-triangular matrices. Let B= a basis for V. (You do not need to prove this.) (a) (8 points) Use the Gram-Schmidt procedure on 3 to find an orthonormal basis for V. Find projy (B) (b) (4 points) Let B=
4. Consider R2x2 with inner product (A, B) tr(ATB), and let V CR2x2 be the subspace 1...
Q5 Eigenmatrix 8 Points Let C12 M2 = 211 221 : Xij ER ER} 2 22 be the vector space of 2 x 2 real matrices with entrywise addition and scalar multiplication. Consider the subspace W = {X E M2 : X = XT} of M2 consisting of symmetric matrices. (a) (2pts) Find a basis of W. What is its dimension? 1 (b) (2pts) Let A= Show that if X EW then AXAT EW. (c) (4pts) Consider the linear transformation...
(1 point) Let Ps be the vector space of all polynomials of degree at most 3, and consider the subspace 11 = {r(z) e Pal p(1) = 0} of P3 a A basis for the subspace H is { 22x+12x^2-x-1 Enter your answer as a comma separated list of polynomials. b. The dimension of His 3 (1 point) Find a basis for the space of symmetric 2 x 2-matrices If you need fewer basis elements than there are blanks provided,...
2. Let M2x2(R) be the vector space consisting of 2 x 2 matrices with real entries. Let W M2x2 (R) det (A) 0. Show that W is not a subspace of M2x2(R) A E
Let V = M2x2 be the vector space of 2 x 2 matrices with real number entries, usual addition and scalar multiplication. Which of the following subsets form a subspace of V? The subset of upper triangular matrices. The subset of all matrices 0b The subset of invertible matrices. The subset of symmetric matrices. Question 6 The set S = {V1, V2,v;} where vi = (-1,1,1), v2 = (1,-1,1), V3 = (1,1,-1) is a basis for R3. The vector w...