Let A € Mnxn (R), & be the standard basis for R", and B = {₁,...,n} be another basis for R". If P is the change of coordinate matrix from B-coordinates to E-coordinates, then prove that [[A₁]BAU₂]B] = P-¹AP.

Q: Let A be a 3 x 3 matrix such that B Find a non-zern vector Null(AT) -5 is a basis of Col(A).

A: Given : Let A be a 3×3 matrix and  B=5-5-2 , -54-2 be the basis of ColA To Find : A non-zero vector…

Q: Let B = {B]. A} mation x→→ Ax. =[%] be a basis for R2 and A = Find the B-matrix for the transfor-

A: Given that The transformation is

Q: 2. Find a vector orthogonal to the nullspace of the matrix [1 27 6. 4 L5 -1 2.

A: According to the given information it is required to find a vector orthogonal to the null space of a…

Q: 10. For a new basis system the two basis vectors are E',E,+E₂+E, E'=E,-E, where E is 1 1 the…

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Q: Given the coordinate matrix of x relative to a (nonstandard) basis B for R, find the coordinate…

A: We will find the coordinate of vector x with respect to the standard basis as follows

Q: Find a basis of the linear space V of all 3 x 3 matrices A for which both | - A 1 and are…

A: We have to find the basis of linear space V.

Q: - Determine if S = {[1246]} 0 forms a basis for M2,2.

A: We know that M2×2 is a vector space of all 2×2 real matrices over R.Given that .We need to determine…

Q: → Suppose TR³ R³ be a linear bronsformation whose standard matrix has the basis (o 1, 2), (2, 1…

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

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Q: 10. Let A be a nonsingular n xn matrix, and let B be a basis for R". (a) Show that B1 = {Av | v € B}…

A: The complete solution is in given below

Q: Suppose {u₁, U2,..., U2n} is an orthonormal basis for R2n. Let n A = Im - Σuju?. j=1 Show that (a)…

A: We show that A is idempotent matrix   For this we have A2 =A .. And the eigen values of idempotent…

Q: Find the coordinate matrix of x relative to the orthonorm x = (10, 20, 5), B = {(÷, 0). (- ÷ [x]B =…

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Q: now that B = {x, r³ + 2x² + 4, x² + 2, 1} is a basis for P3.

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Q: Consider B = the standard basis for IR, and B' = another basis for R. For these bases: Part (a):…

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