Question

Struggling with these two. help me please

Use Cramer's Rule to solve (if possible) the system of linear equations. (If not possible, enter IMPOSSIBLE.) 4x - 2y + 32 = -7 2x + 2y + 5z - 13 8x - 5y - 22 = 1 (x, y, z) = ( IMPOSSIBLE *) Need Help? Read It Talk to a Tutor Submit Answer Practice Another Version 12. -14 points LarlinAlg8 3.4.027. My Notes Ask Your Teacher Use Cramer's Rule to solve the system of linear equations for x and y. kx + (1 - k)y - 5 (1 - k)x + ky = 4 For what value(s) of k will the system be inconsistent? (Enter your answers as a comma-separated list.)

Answer 1

4X - 24 + 37 = -7 2. I + 2y +57 = 13 836 -54 - 22 = 1 system in We will first it write this matrix form. :54 -2 37 12 2 5 1 y = 18 - -2 1-7 N + X - and A = {C, on co] 14 12 18 -2 2 -5 31 5 -2] Given system is AX = b Scanned with CamScanner

We first find f det (A)=0 for dependent det (A) then =D (say) system is inconsistent 31 w D = det (A) = 14 -2 D = al 11 - 12 2 Ň G 246-4+25)-(-2)(-4-40)+ 3(-10-16) = 4X21 + 21-44) + 3(-26) = -82 Dt0 = system is consistent & Solution is possible Wow we will find three more determinants Dx Dy, Dr. where Dx = 16 cq csl ; Dy = 1a, 6 cs/ De = 10, aq bl and then 12 Y , Z P2. Scanned with CamScanner

1-7 -2 31 2 5 Da W ง It -5 - 21 - [7) (-4+25) +2 (-26-5)+36-65-2) = (-7) (21) +2(-31) +36-67) = - 410 14 -7 31 12 13 5 = 4(-26-5) +7(-4-40) + 3(2-104) = 4 (-31) + 7 (-44) + 3(-102) = -738 14 -2 -7 Dy = 12 2 .18 -5 13 11 = 4 (2+65) +2(2-104)-7(-10-16) = 4(67] +2 (-102) - 71-26) = 246 Scanned with CamScanner

- 4 -22 Z = 246 - - 3 : &c het 2 = 5 yes 3D 2016-3 |(2,4,7) = 65,9,-3) (12) Kæ+ (-K)y - 5 (1-K) & + Ky - 4 157 A = I-K Du ln K 1 EKO-(1+60–*) = 2K-1 * = 5K -(4)(1K) = 5K - 4+ 4 K = gk - 4 Scanned with CamScanner

5 og Ik 1-K 4 = 4K-511-K) = 4 K -5+5K =9k-5 gk - 4 qK-1 I gk - 5 2K-1 System is inconsistent D=0 -) AR-) = 0 | Note: so If D=0 then system is inconsistent . or dependent." and if D=0 and also one of the Da iDy is o then dependenti But here for x = 1/2 Da to,Dy to system is NOT dependent... CS Scanned with system is inconsistent at kali CamScanner