1.) Given a matrix A of size 3 × 2 with (image 1) Determine the result of AT × A, A × AT, dan |A × AT|.   2.) Using the inverse of the matrix find the solution of the system of equations 2x + 3y + 4z = 10 x − 21y + 3z = −2 x − y − z = 26

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

(a) A is a 3 x 3 matrix and 2(A + I) = I. Enter det (A + I). (b) A is a 2 x 2 matrix and 2 A + 5 I = 0. Enter det (4+ I). (c) A is a 4 x 4 matrix and 42 - 4 A -21 1= 0. If det (A-21) > 0, enter det (4-21).

2x+y+z=7 4x−3y+2z=4 3x+2y−2z=5 Write the system in matrix form Ax=B. Determine the inverse matrix A−1. Use the inverse matrix to find the solution vector x.

I. Consider the following linear system: 3x1 + 9x2 + 3x3 = 6 2x1 — 2х1 — 4x2 X3 = 12 = -8 We can view this system as a matrix equation: 3 9 31 0 -1 2 12 -2 -4 Which has the form: Ax X = B To solve the original system, we can solve this equation for X by multiplying by A-1: A-1x (A x X) = A-! × B (A-1 × A) × X = A-1 × B Iz x X = A-1 × B X = A-1 x B Use the bottom equation to solve for X. Find A-1 for the matrix A and solve the original system by using A-1 and Bin the (1) equation below. X = A-1 x B (2] Use the matrix A² you just found to solve the system: 3x1 + 9x2 + 3x3 = 12 2x1 -2x1 – 4x2 X3 = 9 = -3

Consider the following linear equations: -5x + 5y +7z : 3 = 5 -5x+(21-k)y + 6z -5x + 5y + (11- k)z =k+11 a) X1 Suppose the above equation is expressed as Ax = b with x = X2 X3 equations in one matrix form as (A[b)= -5 5 7 124 -5 -5 Express the coefficients of the 3

solve all 132

Consider the system of linear equations given by:2x1+ x2− 3x3=8−x2​+ 2x3​=−4 9x1​+ 4x2​− x3​=9 Write the system in matrix form Ax=B. Calculate the determinant of matrix A (∣A∣)