[10 pts) The set {A E R2x2 | A is nonsingular} is a subspace of R2x2.
Problem 2 (10 pts) For a fixed matrices B, C e R2x2, let W = {A € R2x2 | A * B = 2A *C}. Determine if W is a subspace of R2x2 (either prove that it is, or show via specific counterexample that it isn't).
Problem 2 [10 pts] For a fixed matrices B, C e R2x2, let W = {1 € R2x2 | A*B=24*C}. Determine if W is a subspace of R2x2 (either prove that it is, or show via specific counterexample that it isn't).
For the following six questions, indicate whether the following statements are true or false. In each case give a reason for your answer. Problem 13 [10 pts) If L:V +W is a linear transformation of vector spaces and U CW is a subspace of W, then {v € V | L(v € U} CW is a subspace of V. Problem 14 (10 pts) The set {A E R2x2 | A is nonsingular} is a subspace of R2x2. Problem 15 (10...
Is Wa subspace of R2x2? Give a detailed general proof if your answer is yes or a specific counter example if your answer is no. W = {A € R2x2 | det(A) = 0}
1. Prove that each of the following is a subspace. (a) W = {x: x = (x 1, 22, 23) and X1 + 12 = x;} (b) W = {p: p(t) = ata + b + c and a+b+c=0} (C) W = {A € R2x2 and A is upper triangular) (d) W = {f:f EC(0,1) and f(0 =0} 2. Show that the following subsets of A R2x2 are not subspaces. (a) W = {A : A is the singular matrix}...
Is Wa subspace of R2x2? Give a detailed general proof if your answer is yes or a specific counter example if your answer is no. W={A € R2*2 | det(A) = 0}
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...
Question 6 10 pts What is the dimension of the subspace of M22 (R) spanned by the set of 4 vectors şfi 01.1 110 1111 -21} IO 1]'1 0 LO 11-1 1 JS
Determine whether the set together with the standard operations is a subspace of M2,2. Justify the answer: Determine v nine whether the set, together with the standard opera andard operations 1 b 1, where a, b and c are real numbers perations is a subspace of M. You your answer. This is for parts a) and b) only a) The set of all 2 by 2 matrices of the formla (5 points) andarderations is a subspace of M The set...
Let be the set of third degree polynomials Is a subspace of ? Why or why not? Select all correct answer choices (there may be more than one). a. is not a subspace of because it is not closed under vector addition b. is a subspace of because it contains the zero vector of c. is not a subspace of because it is not closed under scalar multiplication d. is a subspace of because it contains only second degree polynomials e. is...