W = Find w if (w)s= 4 11] H 0 relative to the basis S = { 3 ☐☐☐ -3 } 3 -2

Q: Consider the following ordered basis for P₂ (R): B {x²+2x+1, x + 1,1} [] 3 2 (a) What quadratic…

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: Find each of the following Given: u = ; v = ; w = 1. u.v 2. (u.v)w 3. u.(2v)

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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: Determine whether the following set of polynomials forms a basis for P3. Justify your conclusion. P,…

A:

Q: Determine whether b is in col( A) and whether w is in row(A)

A:

Q: Let A = - 7 -6, b 3 2 = [4].. and c = Select true or false for each statement. [1] 1. The vector c…

A:

Q: Suppose |||| = 5 and |||| = 6, and assume and y are orthogonal. Then ||-||²7

A:

Q: Verify that (AB)T = BTAT.

A:

Q: asis: The set B = {2-3x², 8+x-12x², 33x² - (21+ 2x)} is a basis for P₂. Find the coordinates of p(x)…

A:

Q: b Let a = (-3, 0, -1) and 6 = (3, -3, -2). Find the component of b onto a.

A:

Q: If v + w = [ 5/1 ] and v - w = [ 1/5 ],compute and draw the vectors v and w.

A: Vector: An object which has both magnitude as well as direction is called a vector. We can draw a…

Q: Find the canonic analytical expression of the following quadratic form q: R³ → R, q (x) = 6x,²+x,² –…

A: Given quadratic equation is…

Q: Perform the vector addition: (- 3, – 5) + ( – 1, 9) =

A:

Q: Let A = [1 -1 -1              -1   1 -1              -1  -1  1]. Find a diagonalization if possible.

A: We first find the eigenvalues and eigenvectors of A.Start from forming a new matrix by subtracting λ…

Q: Find ß so that {1, x, 1+ 6x²) on (-1,1) is orthogonal.

A:

Q: Let v = (60, – 5, – 5) and w = (– 4, – 30, 22) be ordered triples in R°. Find two scalars c and such…

A:

Q: the polynomials t3+ t² + 1, t? – t + 2, t3 + 2, -t³ +t? – 5t + 2 span P3

A: