Define T: R2→R² by T(x) = Ax, where A is the matrix defined below. Find a basis B for R2 with the property that [T], is diagonal. -3 A = 12 ..... 1 , [T]B B= 1

Q: Find the matrix A′ for T relative to the basis B′.T: R2→R2, T(x, y) = (x − 2y, 4x), B′ = {(−2, 1),…

A: Given that  T: R²→R², T(x, y) = (x − 2y, 4x), B′ = {(−2, 1), (−1, 1)}

Q: The set B = {1-1², 2t-12², 1-1-1²) is a basis for P2. Find the coordinate vector of p(t) = 3 +…

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Q: d) Consider the linearly independent vectors (1, -2,3,-4) and (1, 1, 2, 2) in R¹. Ex- tend {(1,…

A: Consider the linearly independent vectors  and  in .The transformation Now,Represent  as linear…

Q: Let W be the set of all vectors of the form 4r3s+t 2s 2r t - - 4s 2r 3t - - - (r+5s) with r, s and t…

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Q: Find the specified power of A, the standard matrix for T.T: R3→R3, reflection in the xy-plane. Find…

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Q: 6. Let V = span{1+ x², x}. Two ordered bases for V are Si = {1+x², x} and S2 = {1+x + x?, 2 + x +…

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Q: 2. Define two ordered bases B = and E = on R³. (i) Find the vector vị of R³ whose component vector…

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Q: Let B = {1+t, t – t2, 2t + t2} be a basis for P2. Find [-3+t – t°]B. %3D

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Q: Let B = vector of 7 = E [V]B 0 1 00 {[%] [83] [28] [89]} 9 9 relative to B. -5 -2 || be an ordered…

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Q: Consider the following two ordered bases of R²: [id] B = [id] = {(-1,-1), (-3,-2)}, a. Find the…

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A: Solution.

Q: Find the matrix A of T so that T ([]) = A[]₁

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Q: Let B and C be bases for R2, where C= [8] -[7] [8] · Let B = u₁, U₂. Find the following vectors. x =…

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Q: The set B = = {1 − t², t+t², 1 + 2t-t²} is a basis for P₂. Find the coordinate vector of p(t) = 5 +…

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Q: Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² R²:…

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Q: Find the matrix A' for T relative to the basis B'. T: R2 → R2, T(x, y) = (x − y, 5y − x), B' = {(1,…

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Q: [2x + y] [x – E) = - 3l: (Show all work in this problem.) a. Find the matrix of F with respect to…

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Q: []B = Find the coordinate vector of = 2 4 with respect to the basis B = [1] 0 {CC)6]} 2 for R³.

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Q: Given the basis B = the basisi B | {Q.B]} Find the change of coordinates matrix from the standard…

A: We find required matrix.

Q: Suppose A is the matrix for T: R³ → R³ relative to the standard basis. Find the diagonal matrix A'…

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Q: 6. Let V = span{1+x²,x}. Two ordered bases for V are Si = {1+a², x} and S2 = {1+x + x², 2+ x + 2a²}.…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.