1.6 Questions 15 on paper please 11. 4x₁7x₂ = b₁x₁ + 2x₂ = b₂i. b, = 0,iii. b₁ = -1,b₂ = 1b₂ = 3ii. b, = -4, b₂ = 6iv. b, = -5, b₂ = 1x₁ + 3x₂ + 5x3 = b₁-x₁ - 2x₂=b₂2x₁ + 5x₂ + 4x3 = bzi. b₁ = 1,b₂ = 0,b₂ = -1ii. b₁ = 0,b₂ = 1,b₂ = 1iii. b, = -1,b₂ = -1,b3 = 0In Exercises 13-17, determine conditions on the b's, if any, in orderto guarantee that the linear system is consistent.13. x₁ + 3x₂ = b₁14. 6x₁4x₂ = b₁3x₁2x₂ = b₂-2x₁ + x₂ = b₂15.16.x₁2x₂ + 5x3 = b₁4x₁5x₂ + 8x3 = b₂X₁2x₂x3 = b₁-4x₁ + 5x₂ + 2x3 = b₂-4x₁ + 7x₂ + 4x3 = b₂-3x₂ + 3x₂3x3 = b317.X₁-2x₁ + x₂ + 5x3 +-3x₁ + 2x₂ + 2x3 =X₂ + 3x3 + 2x4 = b₁x4 = b₂2x₁ = b34x₁3x₂ + x3 + 3x4=b418. Consider the matrices[21 27X1A = 22 -2and x = x₂31 1X3a. Show that the equation Ax= x can be rewritten as(A-I)x= 0 and use this result to solve Ax = x for x.b. Solve Ax = 4x.In Exercises 19-20, solve the matrix equation for X.1-12 -157819. 23 0 X = 4 0-30102 -15 -721-20[4 320.0 -1 -1 X = 6 71 1-4Working with Proofs12.43tem can be written intion to Ax= 0. Prosolution.24. Use part (a) of TheTrue-False ExercisTF. In parts (a)-(g)false, and justifya. It is impossiexactly twob. If A is a sqhas a uniqumust havec. If A and 1BA=In.d. If A andsystems Ae. Let A bmatrix.then Sxf. Let A bra uniqumatrix2 189[1 3 7 9g. Let AinvertWorking wiT1. Colors invision scmodels."mixingthe YICby mixiof a chrconverplished

Question

1.6 Questions 15  on paper please 11. 4x₁7x₂ = b₁x₁ + 2x₂ = b₂i. b, = 0,iii. b₁ = -1,b₂ = 1b₂ = 3ii. b, = -4, b₂ = 6iv. b, = -5, b₂ = 1x₁ + 3x₂ + 5x3 = b₁-x₁ - 2x₂=b₂2x₁ + 5x₂ + 4x3 = bzi. b₁ = 1,b₂ = 0,b₂ = -1ii. b₁ = 0,b₂ = 1,b₂ = 1iii. b, = -1,b₂ = -1,b3 = 0In Exercises 13-17, determine conditions on the b's, if any, in orderto guarantee that the linear system is consistent.13. x₁ + 3x₂ = b₁14. 6x₁4x₂ = b₁3x₁2x₂ = b₂-2x₁ + x₂ = b₂15.16.x₁2x₂ + 5x3 = b₁4x₁5x₂ + 8x3 = b₂X₁2x₂x3 = b₁-4x₁ + 5x₂ + 2x3 = b₂-4x₁ + 7x₂ + 4x3 = b₂-3x₂ + 3x₂3x3 = b317.X₁-2x₁ + x₂ + 5x3 +-3x₁ + 2x₂ + 2x3 =X₂ + 3x3 + 2x4 = b₁x4 = b₂2x₁ = b34x₁3x₂ + x3 + 3x4=b418. Consider the matrices[21 27X1A = 22 -2and x = x₂31 1X3a. Show that the equation Ax= x can be rewritten as(A-I)x= 0 and use this result to solve Ax = x for x.b. Solve Ax = 4x.In Exercises 19-20, solve the matrix equation for X.1-12 -157819. 23 0 X = 4 0-30102 -15 -721-20[4 320.0 -1 -1 X = 6 71 1-4Working with Proofs12.43tem can be written intion to Ax= 0. Prosolution.24. Use part (a) of TheTrue-False ExercisTF. In parts (a)-(g)false, and justifya. It is impossiexactly twob. If A is a sqhas a uniqumust havec. If A and 1BA=In.d. If A andsystems Ae. Let A bmatrix.then Sxf. Let A bra uniqumatrix2 189[1 3 7 9g. Let AinvertWorking wiT1. Colors invision scmodels.&#34;mixingthe YICby mixiof a chrconverplished

Accepted Answer

Using fact that system is consistent iff rank(augmented matrix)=rank( coefficient matrix)

13. 14 x₁ + 3x₂ = b₁ -2x₁ + x₂ = b₂ : 15. x₁2x₂ + 5x3 = b₁ 16 4x₁5x₂ + 8x3 = b₂ -3x₂ + 3x₂ - 3x3 = b3 17. X₁ X₂ + 3x3 + 2x₁ = b₁ -