Let E = {(1,0,0), (0, 1, 0), (0, 0, 1)} and S = {(1,0, 1), (1, 1, 2), (1, 2, 4)}, bases for R°. (a) Find P, the change of basis matrix from E to S. (b) Find Q, the change of basis matrix from S to E. (c) Verify that Q = P-1.

Q: The third column of the change of basis matrix from the basis B={u= (1,1,1); v= (1,0,1); w= (0,1,1))…

A: Given the basis             B=u=1, 1, 1, v=1, 0, 1, w=(0, 1, 1), to the basis,            B'=r=(3,…

Q: Given that [x]B -5 is the coordinate matrix of x relative to a (nonstandard) basis…

A:

Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

A:

Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: Find the coordinate vector[x],of x relative to the given basis B= {bl,., bn}. --]--[}]--[1] bị = ,b2

A:

Q: EXAΜPLE2 Determine whether the vectors vi-(1,-2,3),v2=(5,6,-1),v3-(3,2,1) are linearly independent…

A: Given vectors are v1 = (1, -2, 3), v2 = (5, 6, -1), v3 = (3, 2, 1)

Q: Find the matrix of the standard inner product on W (obtained by restriction of the dot product on…

A: “Since you have asked multiple questions, we will solve the first question specified by you i.e.…

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

Q: Find the coordinate matrix of x in Rn relative to the basis B′.B′ = {(8, 11, 0), (7, 0, 10), (1, 4,…

A:

Q: 3-1 Let P -3 -5 and v 3 Complete parts (a) and (b). 15 a. Find a basis (u, U, U) for R'such that P…

A: Step:-1 Given that  P=13-1-3-50451,  v1=-425,  v2=-743,  v3=-935 Take  B=u1, u2, u3  and  B'=v1, v2,…

Q: The coordinate vector of the (-4,3,1) in the B={u= (1,1,1); v = (1,0,1); w=(0,0,1)} is : A. (-4,3,1)…

A:

Q: 1. Say whether the following vectors are linearly independent and whether the vectors form a basis…

A: Given Data: Let us consider the given data, c 2,-2,1,0,2,-2,2,0,-1d 1,1,1,1,-1,-1,-1,1,-1,-1,-1,1…

Q: Apply Gram-Schmidt orthogonalization to the column vectors of A, a1 = (1, 1, 0)T ,a2 = (1, 0, 1)T ;…

A:

Q: orthonormal 3D vectors

A:

Q: #7. Given that the three 3-dimensional vectors v1 = (- 1,3, - 4), v2 = (3, – 8, 10), v3 = (2, – 9,7)…

A:

Q: Determine whether the given vectors are form a basis of 3 V₁ = (3,-1,2), 2 (6, -2,4), V3 = (5,3,…

A:

Q: Find the coordinate vector for w relative to the basis S= {u1, u2} for R2. uj = (1, 0), u2= (0, 1);…

A: Here we use basic defnition of change of basis coordinate

Q: Find the coordinate vector of v relative to the basis S = {v1, V2, V3 } for R3. v = (-1, –10, 6); v1…

A:

Q: Find a set of vectors {ū, v} in R* that spans the solution set of the equations w – x 4z 0, 2w + 2x…

A: We have four unknown variables (w,x,y,z) and two equation. This emply there are two free variables.…

Q: Determine if the vectors vị = (1, –1,3, –1), v2 = (1, –-1, 4, 2), v3 = (1, –1,5, 7) are linearly…

A: We have to determined the vectors v1=(1, -1, 3, -1), v2=(1, -1, 4, 2), v3=(1, -1, 5, 7) are linearly…

Q: In P2, find the change-of-coordinates matrix from the basis B= {1 − 2t + 1²,3 −5t + 4t²,2 − 2t +…

A:

Q: Let u = (1,3, 5) and v = (-4,3, –7) be vectors in R3. (a) Find u + v. (b) Express u in terms of the…

A:

Q: Consider the following matrix: 2 -2 4 6 6 A = -1 1 3 2 -3 -1 1-3 -3 1 Give a basis for each of…

A:

Q: Find the coordinate vector (v)s relative to the basis S= {v ,,v,,v;} 21 for v = (2, 1, -2), if V=…

A:

Q: Either find the coordinates of the vector relative to basis B, or find the original vector from the…

A:

Q: Find the determinant of the vectors (2,4,0),(0,4,6),(8,0,6) with respect to the base…

A: Let  S = (2 4 0), ( 0 4 6) , (8 0 6)                      α1          α2          α3&      T =…

Q: Find the coordinate vector of v relative to the basis S = {v1, V2, V3 } for R3. v = (41, 39, 21); v1…

A:

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.