3. Let V be the subspace of M2x2(R) consisting of all matrices in which the sum...
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...
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).
How can I get the (a) 3*2 matrix A? x 7. [30pts] Let V be the subspace of R consisting of vectors satisfying x- y+z = 0 y (a) Find a 3x2 matrix A whose column space is V and the entries a a1 0 = (b) Find an orthonormal basis for V by applying the Gram-Schmidt procedure (c) Find the projection matrix P projecting onto the left nullspace (not the column space) of A (d) Find an SVD (A...
(a) Determine a basis for the subspace of M2x2(R) spanned by A-[-1.),B=(-4c-[i 1.0- [5 1]. (b) Let S be a subspace of the vector space R3 consisting of all points lying on the plane with the equation 20 + 4y - 32 = 0. Determine a basis for S and extend it to a basis for R3.
(1 point) (a) If S is the subspace of M3(R) consisting of all lower triangular matrices, then dim S = (b) If S is the subspace of M4(R) consisting of all skew-symmetric matrices, then dim S =
Let w be a subspace of R", and let wt be the set of all vectors orthogonal to W. Show that wt is a subspace of R" using the following steps. a. Take z in wt, and let u represent any element of W. Then zu u = 0. Take any scalar c and show that cz is orthogonal to u. (Since u was an arbitrary element of W, this will show that cz is in wt.) b. Take z,...
be the vector space of all two-by-two real matrices. Is either of these subsets a M2x2 1. Let V subspace of V? Justify ( 2) a The set of matrices such that ad d (a) = -1. The set of all two-by-two matrices with zero determinant (b)
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...
2. Let W = { A € M2x2(IR) trace(A) = 0} W2 = { A € M2x2(IR) A = AT ). a) Show that W C M2x2(IR) is a subspace and find a basis for W. b) Find a basis for WinW2 and compute its dimension.