How do I find a basis for {(2c, c, b)} | b, c ∈ R}? I tried writing it as a linear combination and I get: (2c, c, b) = a(0,0,0) + b(0,0,1) + c(2,1,0). Clearly, this contains (0,0,0), which means this is linearly dependent. Hence, it cannot be a basis. Note: Please refrain from using matrices and explain through equations/linear combinations as much as possible.

Q: et B = · 9, (x − 1)², 3x³) be an ordered basis for P3. Find the coordinate vector of (x) = 3x³ + 2x²…

A: Coordinate vector

Q: A)  Justify if the matrix A is diagonalizable.B)  Find a matrix T and a diagonal matrix J, such that…

A:

Q: Consider the ordered bases 3 = {(1,0), (1, 1)} and ß' = {(1,7), (–2, 5)} for R². (b) Let 3" = {v1,…

A:

Q: Find the matrix A' for T relative to the basis B'. T: R2 > R2, T(x, у) 3 (x — у, 2у - х), в' %3D…

A:

Q: y Suppose E (A, B) is controllable. Suppose a change of basis is performed so that we obtain a new…

A: As per the question we are given a controllable system as : ∑ ➞ (A, B) And after a change of…

Q: 2) Let T a d 11 la + 2b + (-6) c + 2d + (-18) e 2a + 5b+ (-14) c + 6d+(-46) e Then a basis for…

A:

Q: TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT

A: Given that

Q: Consider the basis B = {t^2 −2t+1, 4t^2 −5t+3, 3t^2 +2t} for P2. Compute (2t−1)B by setting up and…

A:

Q: Explain how fixing a basis v1, corresponding function in n variables of the form q(x1, · ·· , Xn) =…

A:

Q: B=[(1, 2, 1)", (0, 1, -1)', (1, 1, 1)"] is an ordered basis for , C =[(1, 1)', (2, 3) '] is an…

A:

Q: Find the matrix A' for T relative to the basis B'. T: R > R, Tх, у, z) %3D (у — z, х - z, х + у), В'…

A:

Q: 6 Let b₁=[2] b₂ = 3 4 [ C₁ = [ ² ] ² ₂ = 1²²] > V = [] (2 13 2 and C = { C₁₂ (₂} Find and consider…

A:

Q: Example 3: Find the coordinate matrix of x (3, 19, 2) in R³ relative to the basis B' = {(8, 11,0),…

A:

Q: Find the coordinate vector of p(x) in P., relative to the basis S= {p,.P.-P;}, where p(x) =…

A:

Q: In P2, find the the standard basis C = {1,t,t²}. Then find the B-coordinate vector for 1 - 2t + 2t².…

A:

Q: 3. For each of the following pairs of ordered bases ẞ and ẞ' for P2(R), find the change of…

A: To find the change of coordinates matrix from a basis β′ to β for the vector space VThe identity…

Q: Let R2x2 be a linear space with all 2 × 2 real matrices. (1) Find a basis of R22 and dim (R²x2); (2)…

A: Given  be a linear space with all  real matrices.Therefore .We need to find the basis of .The inner…

Q: 4) Let V = M2x2 (C) with standard basis B = (m₁, m2, m3, m4) and let T : V → (a) (b) (c) T((& $)) =…

A:

Q: Question 4: [2 Mark] Determine whether or not the given vectors in R" form a basis for R": a) v₁ =…

A:

Q: Let B = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for…

A: a)b)c)d)

Q: 3) Let C be a basis that contains vectors (−2 + 1x + 1x2 + (−1) x3), (1 + (−2) x + 4x2 + 2x3), (−2 +…

A: