Question

Determine whether S is a subspace or not for the sets below. a) V = ?² : S = {x ? ?² : x? = 1} b) V = ?³ : S = {x ? ?³ : x = ?? a b b-a ?? where a, b ? ? and a = b} c) V = {2 × 2 matrices} : S = {2x2 matrices: with a?? = a?? for i ? j} d) V = ?³ : S = {x ? ?³ : x? = ½x?}

          Determine whether S is a subspace or not for the sets below.

a) V = ?² : S = {x ? ?² : x? = 1}

b) V = ?³ : S = {x ? ?³ : x = ?? a b b-a ?? where a, b ? ? and a = b}

c) V = {2 × 2 matrices} : S = {2x2 matrices: with a?? = a?? for i ? j}

d) V = ?³ : S = {x ? ?³ : x? = ½x?}

Determine whether S is a subspace or not for the sets below.

a) V = ?² : S = x ? ?² : x? = 1

b) V = ?³ : S = x ? ?³ : x = ?? a b b-a ?? where a, b ? ? and a = b

c) V = 2 × 2 matrices : S = 2x2 matrices: with a?? = a?? for i ? j

d) V = ?³ : S = x ? ?³ : x? = ½x?

Added by Tracy J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

06/29/2022

Step 1

To determine if S is a subspace of V = R^2, we need to check if S contains the zero vector. Since the zero vector in R^2 is (0,0), we can see that (0,0) * z = 0 for any z, not equal to 1. Therefore, the zero vector does not belong to S, and S is not a subspace of Show more…

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Determine whether S is a subspace or not for the sets below. a) V = ℐ² : S = {x ∈ ℐ² : x₂ = 1} b) V = ℐ³ : S = {x ∈ ℐ³ : x = (a b b-a) where a, b ∈ ℐ and a = b} c) V = {2 × 2 matrices} : S = {2x2 matrices: with aᵢⱼ = aⱼᵢ for i ≠ j} d) V = ℐ³ : S = {x ∈ ℐ³ : x₂ = 1/2 x₁}