8. Let A = {a₁, A₂, A3} and B = {b₁,b₂, b3} be bases for a vector space V, and suppose α₁ = 4b₁ b₂, A₂ = −b₁ + b₂ + b3, and a3 = b₂ − 2b3. Find the change-of-coordinates matrix from A to B. Use the matrix to find [x] given x = 3a₁ + 4a₂ + a3.

Q: Find values for the the entries in the first matrix to satisfy this equation: 0 0 5 -10 -4 7 0 0 -1…

A: We have to find the entries of the first matrix satisfying the given matrix equation. Let us denote…

Q: Find the matrix of the quadratic form. Assume x is in R°. 5x - 4x3 + 3x3 + 18x,x2 - 4x,×3 b. 3x -…

A: We want to find matrix of given quadratic form.

Q: [-1 -1 21 Let A = = [23] 3 7 Write b as a linear combinations of the columns of A b= a₁t and b a2

A: Given,                A=-12-37, and b=-7-23. To write b as a linear combination of the columns of A.

Q: Diagonalize the following 3x3 matrix. [ {3,3,3},{3,3,3},{3,3,3}]

A:

Q: Determine |z| if z =2−3i.

A: z = x +i*y |z| = √(x2 + y2)

Q: Determine if b [3] 312 1 is a linear combination of a 1 = ------- 0 a2 1, and a3 = 2 6.

A:

Q: Given that −1=−4x−3y and −5=7x+6y, find the values of x and y using the inverse of a matrix. Give…

A:

Q: Given the matrix: A= [1 -2 1 3]. Perform the operation

A:

Q: (Vx + Vx – Vx –

A: