8. Isosceles Trapezoid Conjecture: The base angles of an isosceles trapezoid are congruent. Given: Isosceles trapezoid PART with PA || TR, PT = AR, and TZ constructed parallel to RA Show: LTPA = LRAP Rectangle R A

Find A? if а) А %3D [0, 1, 3}. b) А %3D 1,2, а, b).

Compute: |uv| |||u||||v|| = = |v. w = = ||M||||A|| v= W=

Section 1.3 1 [2] 0 span of a₁, a2, and a3 1. Let a₁ = , a₂ = B. [5]. , a3 = 2 8 and b 6 Determine if b is in the

Recall the definition of Linear Independence: The set {V1,..., Vn} is linearly independent if, whenever a₁ V₁ +...+ an Vn = 0, it must be that a₁ = = an = 0. Suppose that {v2, V3} is linearly independent. Briefly describe what is wrong with the following "proof" that {V1, V2, V3} is linearly independent (where V₁ is some nonzero vector): Since (v2, V3} is linearly independent, a2V2 + α3 V3 = 0. Then, if a₁V₁ + a2 V2 + a3 V3 = 0, we have that a₁ V₁ +0=0 so that a₁ = 0. Therefore, {V1, V2, V3} is linearly independent.

Suppose the product of x and y is 49 and both x and y are positive. What is the minimum possible sum of x and y?The minimal possible sum is

From Linear Algebra Done Right by Axler, how do I prove this for both F=C and F=R? I need to know both proofs and the difference. Appreciate your help!