Let T: P2 → P2 by T(ax? + bx + c) = (12a + 5b – 5c)x² + (-20a – 8b + 10c)x + (10a + 5b – 3c); a the standard basis for P2; ß the basis consisting of x² + 3x, x² – 2, x + 6; v= 4x² + 5x – 2. %3D (a) Find [T]% where a is the standard basis for P,. (b) Find the change of basis matrix from a to ß. (c) Find the change of basis matrix from ß to a. (d) Find [T]. (e) Find [v]g. (1) Find [T(v)]g- (g) Find T(v).

Q: Assume that T is a linear transformation. T: Projects vectors in its domain onto the line y = 2/3 x.…

A:

Q: Find a basis of the subspace of R* defined by the equation 5x1 - 7x2+8x3 6х4 = 0. 9. 9. 9. Basis: 9.…

A:

Q: B = [3 {[9][9]} 02 4 0 56

A:

Q: Find the conjugate of z = u+w If u = 6+2i,z= 1+4i

A: Step 1: The conjugate of a complex number z=a+bi is: zˉ=a−bi i.e., it is obtained by changing the…

Q: Q2] a) Write each (PRODUCT) of the following as a single matrix: i -17 2 -2 -1]-i -2 5] -2| -1 1 -1]…

A:

Q: Let S = {1+ 5x, 1 – 2x-}. Which of the following polynomials could be added to the set S to form a…

A:

Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

A:

Q: Describe geometrically (line, plane, or all of R 3) all linear combinations of (a) [ 1/2/3 ] and […

A: We know that a set of vectors u1, u2, ……, un is said to be linearly independent if the equation…

Q: 5 + 6 x 2- 22 25. 7 3 3 - X 3 3 x 6

A:

Q: Let 13 −4 21. 1 -4 -1 Using a sequence of elementary row operations, transform A into reduced row…

A:

Q: Let a and b be real numbers satisfying a² - a -1 = 0 and 6² - 36 - 2 = 0, and let V = 1 a b ab (a)…

A:

Q: 2x₁ + 4x₂x3 = 15 7x₁3x₂ + 3x3 = -4 4x13x28x3 = 19

A: Given: 2x1+4x2-x3=157x1-3x2+3x3=-44x1-3x2-8x3=19 We have to find the inverse of the coefficient…

Q: For the subspace below, find a basis 9a + 18b3c 3a-b-c -6a +5b+2c -3a+b+c a, b, c in R a. (9,3,…

A: This question is related to topic basis of vector space . Here we have to find basis of given…

Q: Let A 1 2 −1 -2 3 -2 -1 1 1 Diagonalize A to find A100.

A:

Q: Perform the given row operations: 3 7 -8 -87 3-2 -7 R₁ R3 -7-8 5 1) 7

A: We have to perform the row operations as given instructions.

Q: Computations: [7x -3y 9. Compute a basis of x, y E R x + y

A: We will find out the required basis.

Q: Consider the subset of P3 Q = {−6x² + 4x − 6, −24x² + sx + 6, 2sx + s} Find the two values of s for…

A: In this question, we will find the values of 's' for which a given set is linearly dependent.

Q: Use the column-viewpoint to compute the product C = AB of [1 A = 1 = 1² 91 0 -17 1 2 and B

A: Given matrices:- A=1-11102 ,  B=201-1

Q: Find a basis for the solution space  x1+3x2+4x3=0 3x1+8x2+7x3=0

A:

Q: Let A 1 3 = 0 3518 5 - 1 1 020 2 1 1 -2 0 8 - -2 3 Find a basis for the row space of A.

A:

Q: (a) Write a MATLAB program to select and print odd number of the following matrix: [11 23 50 12] 9…

A:

Q: Determine whether B={1-31²,2+t-5t².1+2t) is a basis for P2.

A:

Q: Find a basis of the subspace of R³ defined by the equation 2x1 + 3x2 + x3 = 0.

A:

Q: Consider the ordered basis 3 = {1, 1+ x, 1+ x + x²}. Given that %3D [1+ 2л + За?]8 — (а, b, с)*,…

A: Given β=1,1+x,1+x+x2 And 1+2x+3x2β=a,b,ct We have to find value for a,b and c…

Q: ithout doing any row operations, explain in a short sentence why [137 0506 0028 0 10 A= 1 2 2 31 3…

A:

Q: Notations That Represent A Line

A:

Q: - 3x3 + 7x4 = 0 X1 -7x2 - 4x4 = 0

A: The solution are next step is..

Q: Which of the following matrices have characterestic polynomial p(A) =A-10A+ 1 Select one: O a. T0 1…

A: To find the correct option

Q: T: ([₂]) = 3x1 +4x2 x1 - 2x2 4x1

A:

Q: The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0,1). Find the set A…

A:

Q: Determine a basis for the row space of 3 1 -1 2 -6 4

A:

Q: Find a basis for the column space of -2 4 4 A = 3 3 4 -2 -16 -8

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.