Describe each of the following subspaces as a fundamental subspace of some matrix, and then find an orthonormal basis for them (by any method): (a) U = {ue R5|u is perpendicular to both (1, 0, 0, 1, 0) and (2,0, 1, 1, 1)} (b) V = {(a, b, c, d) = R¹|a + b = c + d} (c) W = the intersection of planes 2x - y + 4z = 0 and -x +2y-z = 0 in R³

Q: Find a basis for the subspace of R3 spanned by S = {(2,3, -1), (1,3, -9), (0,1,5)}

A:

Q: Find the 2 x 2 matrix P such that Po is the orthogonal projection of in R2 onto the line consisting…

A:

Q: Let V be a subset of R³ consisting of all solutions to the linear system x-y-5z=0. Show that V is a…

A:

Q: In the vector space P,, of polynomials of degree atmost two, the matrix of transition from the basis…

A: NOTE: Refresh your page if you can't see any equations. . given polynomials are

Q: a1 For a fixed vector a = a2 E R³, we define the cross product as аз |a2x3 azx2 ахх%— a3X1 – a1x3…

A:

Q: Consider the 2 X 2 matrices A1 =  1      1           A2 =  0      1        A3  =   0      0      A4…

A: Thus, the four matrices are not linearly independent.

Q: In each part, find a basis for the given subspace of R4 .(2) All vectors of the form (a, b, c, d)…

A:

Q: Consider matrix A = (₁ (2) Answer: and vectors x = (-²2) and y = (¹). Calculate matrix B= (A - AT)2…

A:

Q: 1. Consider the vectors (2,-3, 1), (-1,7,-3), and (8,-1,-1). (a) Find a basis for the span of these…

A: (a) Find a basis for the span of the vectors (2,-3,1), (-1,7,-3), (8,-1,-1) showing a row reduced…

Q: Find the orthogonal complement S⊥ of the subspace S of R3 spanned by the two column vectors of the…

A:

Q: Find a basis for the subspace of R'consists of all vectors of the form (a, 2a + b, b, 0). State its…

A:

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

A:

Q: Find the matrix A' = [LA]. Also find an invertible matrix Q such that A' = Q-¹AQ. (a) Suppose W₁ and…

A:

Q: d) If A and B are 4 x 4 nonsingular matrices such that |2A¬'B²| = 32, then |4| = 8 e) Let S =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find a basis of the subspace of R* that consists of all vectors perpendicular to both 0. 1 and 6- 4.…

A:

Q: find an orthogonal basis and then an othnormal basis for the subspace U of R3 spanned by v1 =…

A: The objective of this question is to find an orthogonal basis and then an orthonormal basis for the…

Q: Find a basis for the subspace of R, the plane 2x +y-z+ 3w-0 and convert it into an orthonormal ban

A: Given the subspace 2x+y-z+3w=0. To get the orthonormal basis. The formula for orthonormal basis is,…

Q: Create an example of mathematical formulas of am x n (m =3, n =3) matrix A that relates to Hermitian…

A:

Q: Problem 17: The complement of a fuzzy set S is the set S, with the degree of the membership of an…

A:

Q: Find a basis for the orthogonal complement of the subspace of Rª spanned by the vectors V1 = (3,…

A:

Q: Find an orthonormal basis for the subspace Span ([1, 2, 0, -2], [4,3,0, 2]) of R4.

A:

Q: Find a basis for the solution subspace Ax=0 where A=[-2,4; 1,-2] OA. {(1,0),(0,1)} O B. {(1,2)} C.…

A:

Q: Find the matrix A that represents the usual inner product on R² relative to the basis S on R²…

A:

Q: Let A € Rnxn. Prove or disprove that Ax = 0 and AA x = 0 have the same solution sets.

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Let Y(s) = {y(t)}. Then L{ty"(t)} equals (i) sY (s)- y(0) (ii) s²Y(s) - sy(0) — y' (0) (iii) sY'(s)…

A: Our objective is given below:

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A:

Q: 2. Let {v1, v2, V3}, {w1, w2, w3} be two sets of linearly independent vectors in R³. (1) Show th it…

A: Here we will prove the required result.

Q: (11) Find a basis for the orthogonal complement of the subspace of R" spanned by the vectors V1 =…

A: We have to solve given problem;

Q: Let L be the linear operator on R? defined by L(x1, x2) = (2x1 – 3x2, 21 + 4x2)*:\\ i). Find the…

A: We have to find three matrix A B and P as described in the question.

Q: 4. Consider the set Q of all 2 x 2 matrices A that commute with B = (a) Verify that is a subspace of…

A: