64 = (-12), v = (24) € M₂2 0 M22. Let u = 5.1 Write w = -3 2 -5 2 as a linear combination of u and v. Show all working. 5.2 Is the set {u, v} linearly independent? Explain clearly. 5.3 Is {u, v} a basis for M22? Explain clearly.

Q: Find a basis for R that includes the vectors (2, -1, 5) and (4, 5, -5) {(2, -1, 5), (4, 5, -5), )}

A: Idea is we try to find a vector which is not in the span of given two vectors now collection of…

Q: 8 Let A = {d1, d2}, B = be two bases of a vector space V. Suppose that a2 = -2 b1+3 b 2. Let also…

A:

Q: The set B = {4 – 2x2, 20 – 2x – 10x?, 54 – 4x – 26x²} is a basis for P2. Find the coordinates of…

A:

Q: 7. v₁ = (0, 0, 1), V2 (0, 0, 1), V₂ = (7, 4, 11), V3 = (5, 3, 13) 8. V₁ = V1 (2, 0, 0, 0), v₂ = (0,…

A:

Q: Let B = (v₁.....V₁) be a linearly independent set in R". Explain why B must be a basis for R".

A:

Q: Explain why S is not a basis for R². S = {(-6,4)} OS is linearly dependent. OS does not span R². O S…

A: Given: S=-6, 4. We have to explain why S is not a basis for R2.

Q: Explain why S is not a basis for R2. S = {(-4, 9), (0, 0)} O sislinearly dependent. O sdoes not span…

A:

Q: 6. An n x n matrix A is diagonalizable if and only if it has n distinct eigenvalues. ? 7. Let W be a…

A:

Q: Determine whether {v1, v2, V3} is a basis for a3. R V1 4, v 2 = V 3 = -4 8 -8 -24 Yes No

A:

Q: 5. Determine whether or not the following vectors in R³ form a basis for R³. (a) u (3,-1,2), v=…

A: Any three vectors in R3 forms a basis for R3 if they are linearly independent or we can say that in…

Q: Show that the set S= {(-2,-4), (1, 2)} is the basis of R2 or not?

A:

Q: Determine whether {V₁, V2, V3} is a basis for R³. [] V1 = 1. V2 = 0, V3 = -16 20 pe C

A:

Q: Let T: R3 → R3 be a linear map and S be the standard basis. 0-7:00 m De [2 0 2 Final AT = |2 5 4 SS…

A:

Q: find the change-of-coordinates matrix from the basis In P2, B = {1-3t+t²,2-5t + 3t²,3 − 6t+ 7t²} to…

A:

Q: Determines whether or not the given set of vectors is a basis for the R2 space. Justify your…

A: Given set :(1) (-4,4),(4,8)                    (2) (-1,1),(1,-1)To determine whether or not the…

Q: - 3 HG 4 4 5 1 2 Let P = - 3 1 3 - 1 W₁ = -5 0 - 4₂ = a. Find a basis (U₁, U₂, U3} for R³ such that…

A: (a)It is given that, P is the change of coordinates matrix from to .Also, the values are:So, using…

Q: Determine whether B={1-31²,2+t-5t².1+2t) is a basis for P2.

A:

Q: Explain why S is not a basis for P2. S = {1 - x, 1 - x², -1 - 4x + 5x2} O sis linearly dependent. O…

A:

Q: Explain why S is not a basis for R2. S = {(-6, 6)} O sis linearly dependent. S does not span R². S…

A:

Q: If V1 = [1 4 0] and V2 = [ -2 0 8], then determine all possible 1x3 row vectors V3 such that the set…

A:

Q: Consider the set S: Is this set a basis for R2? Why or why not? What can be said about how can be…

A:

Q: Determine a basis for the row space of 3 1 -1 2 -6 4

A:

Q: a The vector b can be expressed in the basis с 0 0 CHEED-E- -2 -2 -3 as What is -3 -4 0 -2 the…

A:

Q: 1 Determine whether B= {1-3²,2+t-5t².1+2t} is a basis for P2-

A: