Can I get solution for part c 5. Let A =all00a12 a13a22 a230A33.be an upper triangular matrix such that the elements onX₁the main diagonal are non-zero and let x = x₂(a) Solve the equations Ax=0 by starting at the equation for x, and working(9)backwards towards the equation for x₁. (So: the equation for x3 isa33x3 = 0⇒x3=0, The equation for x₂ is a22x₂ + a23x3 = 0 and we know thatx3 = 0, so x₂ = 0, etc.)0(b) Use the same method as in (a) to solve the equations Ax= 1 and Ax= 0(17)(c) Use the results from (a) and (b) to deduce the inverse matrix A-¹.

Answered: Image /qna-images/answer/41e826f8-9234-4348-ad7d-1443c74b33a2.jpg

5. Let A = a22 a23 be an upper triangular matrix such that the elements on 0 A33. all a12 a13 0 0 X₁ the main diagonal are non-zero and let x = x₂ (a) Solve the equations Ax=0 by starting at the equation for x, and working -- backwards towards the equation for x₁. (So: the equation for x3 is a33x3 = 0⇒x3=0, The equation for x₂ is a22x₂ + a23x3 = 0 and we know that x3 = 0, so x₂ = 0, etc.) 0 (b) Use the same method as in (a) to solve the equations Ax= 1 and Ax= 0 -8- (c) Use the results from (a) and (b) to deduce the inverse matrix A¹.

5. Let A = a22 a23 be an upper triangular matrix such that the elements on 0 A33. all a12 a13 0 0 X₁ the main diagonal are non-zero and let x = x₂ (a) Solve the equations Ax=0 by starting at the equation for x, and working -- backwards towards the equation for x₁. (So: the equation for x3 is a33x3 = 0⇒x3=0, The equation for x₂ is a22x₂ + a23x3 = 0 and we know that x3 = 0, so x₂ = 0, etc.) 0 (b) Use the same method as in (a) to solve the equations Ax= 1 and Ax= 0 -8- (c) Use the results from (a) and (b) to deduce the inverse matrix A¹.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.7: The Inverse Of A Matrix

Problem 30E

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