Consider the vector space M2×2 with this basis. Вз βι = -( :). B2 = = (32). - (69). - (4%) Define a map h: M2x2 →R³ by its action on the basis elements. ■) What is h(M)? Він 3 B4 = - 0-0 - 0-0 2 M= († 1) == (} Solution: Is this map an isomorphism? Solution:

What are the coordinates of P(23t/2)? А. (-1, 0) В. (1, 0) С. (0,1) D.(0,-1)

The normal vector of 2 x + By - 16.7z = -8 is: [2, , -16.7, 8 0 [물, 꽃, -16.7, -8] [올, 꽃, -16.71 아올, - 꽃, 16.7.]

Let f([])= -6 u + 6 v be a real-valued function and let - [35] and find that f(z) - = 수 수 수 [23] be vectors. We (no arithmetic permitted in this answer) and f(3) = (no arithmetic permitted in this answer). Ifz--22+5y, then f(3) = (arithmetic is permitted in this answer)

Determine if the list ( [111], [121], [011], [122] ) of vectors from vector space V = R^3 is linearly independent. If yes, show work, if no state a linear combination among the vectors of the list that adds up to a vector in the list. I am having trouble grasping the concept so if anyone can explain this problem I'd appreciate it.

Let V₁, V2, V3 be the vectors in R³ defined by 18 ---D V₁ = -6 V2 = -14 V3 = 20 (a) is (V1, V2, Vs} linearly independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁, V₂, and V3 0 (c) Type the dimension of span {V1, V2, V3}: Note: You can earn partial credit on this problem. -25 -18] 0=v₁+√₂+vs (b) Is (v1, vs} linearly Independent? Write all zeros if it is, or if it is linearly dependent write the zero vector as a non-trivial (not all zero coefficients) linear combination of V₁ and V3. 0=v₁+v₁ V3

5. i ' Find the solution space and write it as a linear combination of vectors. - x3 + 5x4 = 0 X2 + 4x3 – 3x4 = 0 X1

Suppose vector a= (4, -6, 10) and vector B= (-6, 9, -15). What is a x b?

What is the component form of the vector with an initial point of (-2,5) and a terminal point of (7,-3)?

Find a vector that is orthogonal to (−1, 2, 2)