4) Let VM2x2(F) be the set of all matrices of size 2 × 2 and let U and W be two subspaces of V such that U = {[y]: x, y = F} and W = {[ ] : x, y = F}. x Then, show that V = UW.

Q: Which one of the following is a subspace of the vector space M2 (R) of 2 x 2 matrices? ss (X) the…

A: .

Q: Is the set of all vectors (x, y) in R, with the usual addition and scalar multiplication, a subspace…

A:

Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: Let A be an m × ʼn matrix with real number entries. Let N(A) be the null space of A, and let Col (A)…

A: The null space of a matrix A is represented as  where V is thevector space.The transpose of a matrix…

Q: Let X ∈ R3 be some xed vector with coordinates X1, X2, X3. Consider the action on vectors of the…

A: From the given information we get:

Q: Determine the dimension of the subspace of R consisting of all XeR* such that x1 + 2x, = 0 and X3 –…

A:

Q: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

Q: 20) Let W be the vector space of all symmetric 2 x 2 matrices. Show that W sisomorphic to R³

A: Introduction: The set of vectors v1, v2, ..., vn in V is said to be linearly independent if the only…

Q: Let M3,3 denote the vector space of all 3 × 3 matrices. Let L3,3 denote the set of all lower…

A:

Q: Is W=set of upper triangular 3x3 matrices a subspace of V= all 3x3 matrices? Support your answer to…

A: According to the given information, it is required to show that set of all upper triangular matrices…

Q: Let V = R' and define vector addition as (x, y, z)+(x', y', z')= (x+x',y+y',z+z') (standard…

A:

Q: 3 Let M₂(R) be the vector space of all 2 × 2 matrices with entries from R. Show that M₂ (R) = W₁ W₂,…

A:

Q: Determine all subspaces of W.

A: