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A: Topic:- matrix algebra
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A: Let's find.
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A: As per bartleby guidelines we only give first question answers.
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A: We will simplify the problem.
Q: image
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A: First option is correct
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Q: diagram
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- In C[−π, π], find the dimension of the subspace spanned by 1, cos 2x, cos2 x.1. Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector subspace of all 2 x 2 matrices?let S be the collection of vector [x] (3x1 matrix) in R3 that satisfy the given [y] [z] property. In each case, either prove that S forms a subspace of R3 or give a counterexample to show it does not. x-y+z=1
- Find a basis for the two-dimensional subspace of R^4 defined bySuppose that S1 and S2 are subspaces of a vector space (V, F). Show that their intersection S1 ∩ S2 is also a subspace of (V, F). Is their union S1 ∪ S2 always a subspace?let S be the collection of vectors [x] (2x1 matrix )in R2 that satisfy the given [y] property. In each case, either prove that S forms a subspace of R2 or give a counterexample to show that it does not y=2x
- Find the orthogonal projection of 9e1 onto the subspace of ℝ4 spanned by <2, 2, 1, 0> and <-2, 2, 0, 1>.Show that W = {(x1, x2): x1 ≥ 0 and x2 ≥ 0}, with the standard operations, is not a subspace of R2.Let P2P2 be the vector space of all polynomials of degree 2 or less, and let HH be the subspace spanned by 4x2+11x−8, x2+4x−34x2+11x−8, x2+4x−3 and 4−5x4−5x. The dimension of the subspace HH is . Is {4x2+11x−8,x2+4x−3,4−5x}{4x2+11x−8,x2+4x−3,4−5x} a basis for P2P2? Be sure you can explain and justify your answer. A basis for the subspace HH is {{ }}. Enter a polynomial or a comma separated list of polynomials, where you can enter xx in place of x2x2.
- let S be the collection of vector [x] (3x1 matrix) in R3 that satisfy the given [y] [z] property. In each case, either prove that S forms a subspace of R3 or give a counterexample to show it does not. x = y = zFor a linear algebra matrix with initial value, how would I set up a general formula for xk to determine the limit as k approaches infinity for xk?Give an example of a non-zero subspace of R^4 which has dimension > 1 and does not contain any of standard basis vectors e1, e2, e3, e4.