Exercise 5.9.9 Write the solution set of the following system as a linear combination of vectors 0 0 1-181 = 0 0 1 1 3 3 0 1 1 -1 1 0 1 3 2 303 X −1 y Z W Exercise 5.9.10 Using Problem 5.9.9 find the general solution to the following linear system. 1 01 1 1 1 -1 1 0 2 3 1 3 2 4 3 303 3 X y Z W =

Determine if the system Ax=b is consistent. Find a least square solution to 0 2 Ax=b where A = 3 0 b =| 1 %3D 1 13 Also find orthogonal projection of b on to Col A.

2x/5+5x=22/15

Can you write the final answer in particular solution?

I need help with part c

6. LADW #2.2.1bf, page 46 (you only need to do (b) and (f)) - Note that you need to solve the system and write your solution in vector form. You can use technology to help (ie, you do not need to do row reductions by hand), but you shuld show that main steps (ie, what the reduced echelon form looks like and the corresponding system of equations). 2.2.1(b) 2.2.1(f) x12x2x3 = 1 2x13x2 + x3 = 6 3x1 5x2 = 7 x1 + 5x3 = 9 2x1 2x2x3 + 6x4 - 2x5 = 1 x1x2 + x3 + 2x4 x5 = 2 4x1 - 4x2 + 5x3 +7x4 x5 = 6

Find the general solution of the simple homogeneous "system" below, which consists of a single linear equation. Give your answer as a linear combination of vectors. Let x2 and x3 be free variables. 2x1 - 8x2 + 6x3 = 0 O x2 = X₂ 0 + X3 1 (with X2, X3 free) Ox1 x2 = 4x2 x3 Ox1 x2 = X2 1 0 x3 x1 +3x2 (with x2, X3 free) x3 -3 A 1 + X3 0 (with X2, X3 free) 640-8 x2 FX2 1 + X30 (with X2, X3 free)

1. Describe the solutions of the given system into parametric vector form.x1+x2+ 2x3= 9,2x1+ 4x2−3x3= 1,3x1+ 3x2+ 6x3= 27.Also compare this solution, geometrically, with the solution set of the followinghomogeneous system.x1+x2+ 2x3= 0,2x1+ 4x2−3x3= 0,3x1+ 3x2+ 6x3= 0.

Can you help with question 1.5.7?

Exercise 5.9.2 please