In Exercises 27–28, what condition, if any, must a, b, and c satisfy for the linear system to be consistent?
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- In Exercises 13–17, determine conditions on the bi ’s, if any, in order to guarantee that the linear system is consistent. 13. x1 +3x2 =b1 −2x1 + x2 =b2 15. x1 −2x2 +5x3 =b1 4x1 −5x2 +8x3 =b2 −3x1 +3x2 −3x3 =b3 14. 6x1 −4x2 =b1 3x1 −2x2 =b2 16. x1 −2x2 − x3 =b1 −4x1 +5x2 +2x3 =b2 −4x1 +7x2 +4x3 =b3 17. x1 − x2 +3x3 +2x4 =b1 −2x1 + x2 + 5x3 + x4 = b2 −3x1 +2x2 +2x3 − x4 =b3 4x1 −3x2 + x3 +3x4 =b4arrow_forwardIn Exercises 27-28, what condition, if any, must a, b, and c satisfy for the linear system to be consistent? 27. x + 3y - z = a x + y + 2z = b 2y3z = c 28. x + 3y + z = a -x - 2y + z = b 3x + 7y -z = Carrow_forwardApply a theorem from the lecture to determine whether or not the linear system above have a solution besides x=y=z=w = 0. 3x - 2y + 8z + 13w = 0 9x + 11y - 7z - 17w = 0 -15x + 2y - 6z + 21w = 0arrow_forward
- Need help in part b Linear Algebraarrow_forwardConsider the difference equation an+2+an+1+an = 0. (a) Write down the associated discrete linear system n+1 = An- (b) Find a formula for A" and use this to give an explicit expression for an in terms of ao and a₁. [Hint: Note that A" has only 3 values.]arrow_forward8. , determine conditions on the constants b, (b1, b2 etc), if any, in order to guarantee that the linear system is consistent: x1 – 2x2 – x3 = b| -4x1 + 5x2 + 2x3 = b2 -4x1 + 7x2 + 4x3 = b3arrow_forward
- Linearize the following mathematical model: max 3x1 + 5x2 + X1X2 S.t: 2x1 + 4x2 < 150 X1 + x2 < 200 X1, X2 € {0,1}arrow_forward4. Use Gaussian elimination with backward substitution to solve the following linear system: 2x1 + x2 – x3 = 5, x1 + x2 – 3x3 = -9, -x1 + x2 + 2x3 = 9;arrow_forward" determine conditions on the bi's, if any, in order to guarantee that the linear system is consistent."arrow_forward
- " determine conditions on the bi's, if any, in order to guarantee that the linear system is consistent."arrow_forwardEvaluate the following linear system using Cramer's Rule: a. x-3y +3z=-4 2x+3y-z=15 4x-3y-z=19arrow_forward2. a) Given the following system of linear equations: -6+ 10 *+y+=5 2x-y+=9 x-2y+3z =16 Detemine the values of x, y and z using the Cramer's rule.arrow_forward
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