1. Compute u + v and u-2v where u = 2 -5 and v= 1 2

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

A:

Q: Let X = [-1 -1 1] and Y = [0 1 2] consider -1 -21 [a11 XTY = | -1 -2 а32 азз. where X' denotes the…

A:

Q: Find a least-squares solution of A = Ax = b, where 1 2 2 3 −1 2 b = 1 1

A:

Q: Find the least-squares line y = Bo + B1x that best fits the points (-3, -4), (-1, 1), (1,5), (3, 8)

A: Use least square method to solve it

Q: then -A U= 4 5 and uTu · [

A: The given matrix

Q: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

A:

Q: Let A = and v= Verify A(u + v) = Au +Av. 2.

A:

Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

Q: Every combination of v = ( 1 , -2, 1 ) and w = ( 0, 1 , -1 has components that add  to __ . Find c…

A:

Q: 4. Let u = and v = and w = Compute (u x v) x w. %3D 3

A: u×v=ijk-211103=3i-j-6-1+k0-1=3i+7j-k now find u×v×w u×v×w=ijk37-1-111 =7+1i-j3-1+k3+7 =8i-2j+10k

Q: 4. (5pts) Determine if the columns of 3 -2 5 -6 -1 A -6 0 3 4 7 span R'.

A:

Q: 1. Let A=[[4,6], [3,3], [5,7]] and B=[52, 29, 49 ]. Find the least squares solution to A-X' =B O…

A:

Q: Invert the following matrix Зх — 2у — 9 -x + 3y = 3

A:

Q: If u * v = 2i - 3j + k, what is v * u?

A: As we know a×b = - b×a

Q: n2 1 SHOW ALL OF YOUR WORK. 3. an = 2n +1 2n + 1" (а) Find aj, а2, аз, а4. 3 (b) Compute > a;. i=1 4…

A:

Q: Find the least-squares solution of the system 1 -1 -1 1 1 1 -1 1 1 1 2 ||

A:

Q: Compute the following cross products: (а) ј x (3і — ј + 2k); (b) (1,2, 3) х (3, 2, 1); (с) (і — ј+…

A: Let a Vector A→=xi+yj+zk and B→=ai+bj+ck then Cross Product between two vectors A→ and B→ is given…

Q: 7. Set up the linear system that needs to be solved in order to compute the Newton polynomial…

A: We set up the linear system that needs to be solved in order to compute the Newton polynomial…

Q: Compute A5 if A = PDP-1. 1 0 0 2 1 4 P = 0 -1 3 D = 0 0 -1 00-1 A5 =

A: Solution:    Given,    P =1410-1300-1 , D =10002000-1If A =PDP-1 , then we have to find A5=?Now , A5…

Q: Suppose that m>n in the homogeneous system                        a11x1+a12x2+…+a1nxn=0…

A: Here we have a system of homogenous equation with m equations and n variables  Now here m>n which…

Q: 5. Find LU Factorizatioon of A = [5 2 1 1 3 2 7 1 2 3 2 1- Show the work!

A:

Q: #1 Given the following dynamical system: 3 -2 3 Uk = 2 - Ük–1; vo -2 compute i.

A: A square matrix A is diagonalizable if A has n distinct Eigen values. Recall also that if A has n…

Q: Suppose a, = (1 -1 1 1) 5. a, = (1 0 1 0)" a, = (1 1 1 1)'a, = (3 2 3 0)" · Please find out whether…

A:

Q: Compute u – 3v, u v and u x w.

A:

Q: = [4, 3, 0] v = [-2,0, –3] u = u x v = Ex: 5 Ex: 5 Ex: 5

A:

Q: 2 1 Let A = -4 -7 2 36 nd v: Compute Au and Av, and compare them with b. Is it 4 3 possible that at…

A: The matrices are given by: and

Q: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

Q: Compute u + v, 2u – v, 3u – 2v, and 0 – 3v if (a) u =| 2 3 2 (b) u= = -3 (c) u = 1 4

A: (a) Consider the given matrices, u=123 and v=201 now, use the matrices addition property,…

Q: Reduce to Canonical form UTr +5 Ury +6 Uyy %3D

A:

Q: 3- Find the least squares fit of the form y = a, + a,x² to the following data X -1 1 2 y 2 3

A: Given that  The table  By using the least squares to find the equation y