Let A = {a, az, az} and D = (d, d2, dz} be bases for V, and let P = [d•]a [d2]a [d•]a | Which of the following equations is satisfied by P for all x in V? (1) [x]a = P[x]p (ii) [x]p = P[x]A Choose the correct answer below. O A. Equation (ii)is satisfied by P for all x in V. O B. Equation (i) is satisfied by P for all x in V. O C. Both equations are satisfied by P for all x in V. O D. Neither equation is satisfied by P for all x in V.

Q: 4. Let aj = 9. and b = 63 , a2 = 45 (a) Write b as a linear combination of a1 and a2. b = aj + a2.…

A:

Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: Let u = (-3, 1) and v = (0,3). Compute the following: u.v= • = | | i|| 2 = −1 (u · v) • (−1ū) · v ū⋅…

A: Step 1:Step 2: Dot Product (·):The dot product measures how much two vectors are aligned with each…

Q: Let f(x1, x2, X3)=( x1³ + x2, x1² + x3). Find df(1,2,3)(-3, –2, –1).

A:

Q: and B =

A: (2/5,1/5,1/2)

Q: Let u = and v=. (a) Find ||u||. (b) Find u – 3v. -

A: Given: u=1,4,3  and v=2,0,-1

Q: Let ā = (1, 3,-1) and b (-1,0, 2). What is the y-component of ā x b %3D %3D 1 -1 3.

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: () Let z = x + iy. Find Im and Im 2 in terms of x and y. Im Im z2 ||

A:

Q: Given that J(9, -4), K(6, -10), L(1, -1), and M(x, 4), find the value of x so that JK LIM.

A:

Q: Suppose that u · (v × w) = 3. Find (a) u · (w × v) (b) (v × w) · u (c) w · (u × v) (d) v · (u × w)…

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

Q: Let u = = (–3, 3, 5) and v = (−6, −4, −7). Compute the following: ū X x v = v × x ū x ū ū=

A: Please note that as per bartleby guidelines, we need to answer only the first three sub-parts.Kindly…

Q: Let x = (-2,7,-7) and y = (1,6, 6) be in R°. Compute the following: x + y = ( -5x x – y = ( -5 x +…

A:

Q: Show that (AB)T and BTAT are equal.

A: Now,

Q: Find all values of z such that z5 =1 - i.

A: Given: z5=1-i, To find: All values of z.

Q: |

A: vector q is not in the span of vectors.  p1,p2and p3. complete explanation is given…

Q: (a) Let x1,.., Xn+2 € R". Show that there must exist some sets A and B such tha i. ANB=Ø, ii. AUB=…

A: Let x1,x2,....,xn+1∈ℝn We take n=5. then x1,x2,x3,x4,x5,x6,x7∈ℝn There exists two sets A and B,…