In this problem you will solve the nonhomogeneous system B. Compute the inverse Y = C. Multiply by g and integrate | A. Write a fundamental matrix for the associated homogeneous system -1 [v-¹ğ dt = ÿ (Do not include C1 and c2 in D. Give the solution to the system ÿ' = + = your answers). 5 51 -5 3 (Do not include c₁ and c₂ in your answers). C1+ ÿ + If you don't get this in 2 tries, you can get a hint. [2=+] e +C1 +C2 C2

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

2. Consider the system Ax = b with 1 -3 -5 10 -2-48 -3 10 15 A ,b= 50 12 (a) Write down each of the elementary matrices that reduce A to an upper triangular matrix U. (b) Write down the system Ux = c which is equivalent to Ax = b. (c) Solve the system Ux = c for x. No image

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h 9 a ³1² ²₂/+1² 2+1² c d f Express Select one: This cannot be done for all values of a, b, c, d, e, f, g, h as there 8 of these but only 4 unknowns for the entries of the single matrix Oh+a b+e c+d d+fl Oh+2a g+b+e 3c 2d+2f Oh+a_g+b+e C d+f e as a single determinant in a manner that works for all a, b, c, d, e, f, g, h = R. We use | | to denote the determinant. None of the others apply

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∣)

7. In step 2, you solved for the unknowns x, y, and z in Eq. 9. After entering matrices A and b, you calculated the inverse matrix A-1. Then, you multiplied A- and b to find the unknowns. Can you make this process more efficient by using a single “nested" Excel command? Write this command exactly as you would type it into Excel: |