20. Let {u1, uz) be the orthonormal basis obtained by applying the Gram-Schmidt procedure to the basis {1, 12} of Then uz is equal to R2, where r = and r2 = (a) ) (6) (3) () (b) (c) (d) (e) None of the above 21. Which of the following is the equation of the plane passing through the point (2,3, 4) and normal to (a) y -=2 (b) := 4 (c) -z+ 2y + 5: = 0 (d) -z - y = 1 (e) None of the above 22. Which of the following statements about an n x n matrix A is NOT ALWAYS TRUE? (a) A is invertible if and only if its rows span R* (b) The equation Ar = 0 has only the trivial solution if and only if A is invertible (c) A is diagonalizable if and only if it hasn distinct eigenvalues (d) The rank of A is equal to the rank of its reduced row echelon form (e) None of the above these statements are always true

Q: If {e, xe", e2 is a basis of solutions of y" + ay" + by + cy = 0, %3D then a =

A:

Q: If {x, x} is a basis of solutions of a'y" + axy' + by = 0, then b = (A) 3 (B) 2 (С) -3 (D) -2 (E)…

A:

Q: Let Find an orthonormal basis of the row space of A. { [ 1 1 A = [424] -2 -3 ]]. [

A: Row space of a matrix is the vector subspace  spanned by the rows.

Q: It's a Linear Algebra Problem: Execute the Gram-Schmidt process on the following two vectors to…

A:

Q: V is the linear span of the polynomials a =x' + 2x – 2x + 1, ß=x' + 3x² - x+4, y = 2x +x - 7x – 7…

A:

Q: Apply the Gram-Schmidt process to find an orthogonal basis for S. 2 pan{ [ ² ]- [8]} 6 S = span (8)

A:

Q: Find the coordinate matrix of x in R" relative to the basis B'. B' = {(-8, 9), (3, –2)}, x = (-37,…

A:

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: Find the matrix A' for 7 relative to the basis 8'. A' = T: R² R², T(x, y) = (x − y, 4y − x), B′ =…

A:

Q: 4). Find all values of a for which the given vectors form basis for R' -(:) --() ---() a? u = and w…

A: A set B is said to be basis of any vector space if (1) it is linearly independent set. (2)B spans…

Q: Find the matrix A' for T relative to the basis B'. T: R2 - R2, T(x, y) = (-8x + y, 8x – y), B' =…

A:

Q: Find an orthonormal basis of the plane x1 + 8x2 – x3 = 0.

A: That's easy. Have a great day!!!

Q: Find the coordinate matrix of x relative to the orthonormal basis B in R". 3 10 -), (o, 1, 0), 0, 10…

A: To solve the following problem and find the coordinate matrix of x

Q: Consider linear mapping A E L(Vn) and two basis X, Y of Vn. Select all true statements. Let Y be a…

A: Given that, Vn→vector space X=x1, x2, … , xn; Y=y1, y2, … , yn bases of Vn. A∈LV Verify the given…

Q: If the matrix of change of basis from the basis B to the basis B' is 302 A = 20 A. B. - 01 1 column…

A:

Q: Dim (3) Ex. consider T: IR ³ -> R² T( 9₁, 92, ₁₁, 95) = (artastas, 92-94)}. T NCT) = ((a., 92, 93,…

A:

Q: 4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the…

A:

Q: If {e", xe", e2a is a basis of solutions of y" + ay" + by' + cy = 0, then a = (A) -2 (В) 2 (С) —4.…

A:

Q: Let F = sin (7x + 5z)i – 6ye*z k. Calculate div(F) and curl(F). (Express numbers in exact form. Use…

A:

Q: On P(R), consider the inner product given by 1 (p · q) = ["'p(x)q(x) dx. Apply the Gram-Schmidt…

A: Given inner product is Let Using Gram Schmidt Process to make  orthogonal. Let Using Gram Schmidt…

Q: Consider the basis B={(2,1),(-1,2)}. What are the Fourier coefficients of (0,5) w.r.t. B? (1/2,2)…

A: Given- Basis , B=(2,1),(-1,2)To find Fourier coefficients of (0,5) w.r.t. B Suppose ,  Fourier…

Q: Find a basis for the plane 4x + 3y + 5z = 0 in R³.

A:

Q: 9. Let and B 3 = {[B]-[-2]} = B' ={[2¹].[6]} be two ordered bases for R². Find the change of basis…

A:

Q: The vectors p1(t) = 1 + t², p2(t) = −t + 3t², and p3(t) = 1+t+t2 form a basis B 2(t), p3(t)} for…

A:

Q: Consider B={1,x,x^2} and B'={1+x,1-x^2,2} Find the change of basis matrix 1.P from Bto B' 2.Q from…

A: Given bases are B=1,x,x2, B'=1+x, 1-x2, 2 let B'=b1, b2, b3 So change of basis matrix from B to B'…

Q: Apply Gram-Schmidt to (1, 0, −1, 1), (2, 1, −1, 0) , (2, −1, −1, 3) to obtain an orthonormal set…

A:

Q: If x, x is a basis of solutions of r'y" + ary'+ by = 0, %3D then a = (A) -2 (B) 2 (C) -3 (D) 3 (E)…

A: Just use definition of solution of differential equations.

Q: 4. Vector u is a unit vector orthogonal to vectors a and b, where a = i+j-k, b= 2i - j. Then the…

A:

Q: . Find the coordinates of the vector v relative to the ordered basis B. a) B = {x² + 2x +2, 2x…

A:

Q: Answer the following questions: (a) () Find the 12-norms of the vectors, x = (1, 2, 3)T and y = (b)…

A: This is a multiple questions.

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

A: Given vector X is respect of standard order basis.

Q: (1, 2, 1) on to the line x = 2+ t, y = 3 – t, z = t. Also Find Find the Projection of b = Projection…

A:

Q: 2 21 [1] 1 and y = |2 [3. Let u1 = 5 uz and W= Span{u1, U2}. (a) Find an orthogonal basis for W. (b)…

A: Given that, , And, And,…