basis: The set B = {4x² – 3, 16x² − (12 + x), 28 + 2x − 36x²} is a basis for P₂. Find the coordinates of p(x) = 108 + 9x − 140x² relative to this [P(x)] B =

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

A:

Q: The set B = {4x²3, 12x² (9+x), 38+ 3x - 48x²} is a basis for P₂. Find the coordinates of p(x) = 44+…

A: Given; B=(4x2-3, 12x2-(9+x), 38+3x-48x2) p(x)=44+3x-56x2

Q: Show that if B is an n × n matrix with entries in C and  B3=B then B is diagonalisable. Where C is…

A:

Q: If a polynomial p(x) can be factored as a product of two lower degree polynomials p₁(x) and p₂(x) as…

A: It is given that, if a polynomial p(x) can be factored as a product of two lower degree polynomials…

Q: The set B = {4 — 4x², 12 - x - 12x², 33- 3x - 32x² } is a basis for P₂. Find the coordinates of p(x)…

A:

Q: Solve the following set of simultaneous equations using Cramer's rule: X1 + X2 + X3 = 6 X1 – X2 + X3…

A:

Q: X1 3x2 + 5x3 + 15x4 T(x) = |3x₁ + 8x2 − 2x3 − 23x4 4x17x2 + x3 - 16x4

A:

Q: Given basis = {QOB]} {[ 2 5 3 {C₁, C2, C3}. find the basis C = of R³ and change of basis matrix [B]C…

A:

Q: Find the dimension and a basis for the solution space. (If an answer does not exist, enter DNE for…

A:

Q: The set B = {4x? - 1, z -3+ 12z2, 12 – 3x 40x} is a basis for P2. Find the coordinates of p(x) = 52…

A: write each polynomial as a vector  4x2-1=x2x140-1 12x2+x-3=x2x1121-3 -40x2-3x+12=x2x1-40-312 write…

Q: Show that A is diagonalizable.

A: Consider a square matrix A. Then A is diagonalizable if there exists an invertible matrix P such…

Q: The set B = {3 + 2x², 6 − 2x + 4x², 4x − 13 – 10x²} is a basis for P₂. Find the coordinates of p(x)…

A: The objective of the question is to find the coordinates of the polynomial p(x) = 18x - 54 - 40x^2…

Q: If z1 = -4 - j5, z2 = -3 + j2 , and z3 = 2 - j3 , what is Re ( ? Note: z* is the complex conjugate…

A:

Q: For what value of b is the (2 x 2)-matrix A below not diagonalizable over the complex numbers? (b)…

A:

Q: The set B = {− (1+3x²), − (2+2x+6x²), − (6+4x+21x²)} is a basis for P2. Find the coordinates of p(x)…

A:

Q: Find a basis for the solution space of the difference equation. Prove that the solutions found span…

A:

Q: The matrix [50] 02 a) Draw the transformated shape. 5+ 4 3 2 1 -5 -4 -3 -2 -1 is applied to every…

A: Given thatThe matrix  is applied to every point on the unit circle.We have to draw the transformed…

Q: (a) Find A-1. (b) Use answer from (a) to solve Ax = b. (c) Use answer from (b) to express b as a…

A:

Q: Consider the quadratic polynomial q(x) = 2x + 8x1x2 – 8x – 3x1 – 3x2 + 3. - - Find the symmetric…

A:

Q: Find the dimension and a basis for the solution space. (If an answer does not exist, enter DNE for…

A: