9. P = 15 -4 -7 2e31 – 8e- -4e31 + 2e- ž(1) = | 2(1) = 3e3t – 20e- -6e31 + 5et Show that x1 (t) is a solution to the system x = Px by evaluating derivatives and the matrix product -4 ž(1) = | 15 -7 Enter your answers in terms of the variable t. Show that x2(t) is a solution to the system x' = Px by evaluating derivatives and the matrix product 9. -4 K() = | 15 -7

Suppose the above equation is expressed as Ax=b with x=(x1 x2 x3)express the cofficicents of the equations in one matrix form as (A|b)

Consider the following linear equations: -2x + 4y + 10z = -5 -2x + (22-k)y+9z = -3 -2x + 4y+(12-k)z =k+9 a) Suppose the above equation is expressed as Ax = b with x = equations in one matrix form as (Alb)= -2 -2 -2 4 -2 10 4 X3 10 -5 b) Use row operations on (Alb) by substracting row 1 from row 2 and row 3 respectively. Fill in the missing entries: Express the coefficients of the -5 Submit part 3 marks Unanswered

(c) Consider the system 2х1 — бх, — Хз — 38 — Зх1 — х2 + 7Хз :-34 -8x1 + x2 – 2x3 = -20 (i) Write the system in AX = B. 1 0 | and 23/10 1. (ii) Given the decomposition of matrix A is L= -3/2 -4 -6 -1 -43 b -11 -5 a 1 U = (0 -10 and the Al: 11/2 -373/20, -62 373 -11 C -20/ Find a, b and c.