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Solve the following lincar system of oquations using Gaussian Elimination method (1-2) 1. x+ 2y + 3z -3 2x + 3y + 8r 4 Sx + By + 19z = 11

Solve the following lincar system of oquations using Gaussian Elimination method (1-2) 1. x+ 2y + 3z -3 2x + 3y + 8r 4 Sx + By + 19z = 11

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 60EQ
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11. Suppose A(t) = o cost sint show that A(t)- exists and then find it. lo - sint costl Solve the following lincar system of equations using Inverse matrix method (12-13): 12. x + y +z = 6 2x + 3y + 4z = 20 3x - 2y +z = 2 13. x + y +z- 2t = -4 x- 2y + 3z + 4t = 10 2x + 3y - z+ 2t =9 4x - y+ 2z -t= -7 2 1 14. If A =4 -1 2|. find A and hence solve the system of equations 17 3 3x + 4y + 72= 14 2x- y+ 3z = 4 x + 2y - 3z =0 [* +y y+z z +x 15. If A= 2 then compute the determinant of A. 1 16. By using the properties of determinant prove that a e +a a a? + b? 1 2 3 1 -2 3 17. Find the determinant using the row operations o 3 3 2 -1 O D 630 PM 82'F 11/17/2021
Transcribed Image Text:11. Suppose A(t) = o cost sint show that A(t)- exists and then find it. lo - sint costl Solve the following lincar system of equations using Inverse matrix method (12-13): 12. x + y +z = 6 2x + 3y + 4z = 20 3x - 2y +z = 2 13. x + y +z- 2t = -4 x- 2y + 3z + 4t = 10 2x + 3y - z+ 2t =9 4x - y+ 2z -t= -7 2 1 14. If A =4 -1 2|. find A and hence solve the system of equations 17 3 3x + 4y + 72= 14 2x- y+ 3z = 4 x + 2y - 3z =0 [* +y y+z z +x 15. If A= 2 then compute the determinant of A. 1 16. By using the properties of determinant prove that a e +a a a? + b? 1 2 3 1 -2 3 17. Find the determinant using the row operations o 3 3 2 -1 O D 630 PM 82'F 11/17/2021
G Google M inbox strateshat O Reading ist (16) VouTube tacebook Messenger a Meet Solve the following lincar system of equations using Gaussian Elimination method (1-2): 1. x+ 2y + 3z = 3 2x + 3y + Bz=4 5x + 8y + 19z = 11 2. X -* + X- X + Xs1 2x, -X + 3x, + 4xs = 2 3x, - 2x + 2x, + x + Xs =1 X + x + 2x, + X =0 Solve the following lincar system of equations using Gauss-Jordan Elimination method (3-4): 3. x+ 2y - 3z =4 x+ 3y +z11 2x + 5y - 4z = 13 2x + 6y + 2z = 22 4. 10x, - 4x, + X, = 1 X + 4x - X + X, 2 3x, + 2x, + x, + 2x, =5 -3x, - 8x; + 2x - 2x, =-4 X- 6x, + 3x, 1 5. Forward elimination changes Ax = b to a row reduced Rx = d: the general solution is x=0+s1+to What is the 3 x 3 reduced row echelon matrix R and what is d? Find the conditions on a, b, and e so that the following linear system of equations have a solution (7-8): 6. -2x +y +z= a x- 2y +z = x+y-3c O D 630 PM 11/17/2021
Transcribed Image Text:G Google M inbox strateshat O Reading ist (16) VouTube tacebook Messenger a Meet Solve the following lincar system of equations using Gaussian Elimination method (1-2): 1. x+ 2y + 3z = 3 2x + 3y + Bz=4 5x + 8y + 19z = 11 2. X -* + X- X + Xs1 2x, -X + 3x, + 4xs = 2 3x, - 2x + 2x, + x + Xs =1 X + x + 2x, + X =0 Solve the following lincar system of equations using Gauss-Jordan Elimination method (3-4): 3. x+ 2y - 3z =4 x+ 3y +z11 2x + 5y - 4z = 13 2x + 6y + 2z = 22 4. 10x, - 4x, + X, = 1 X + 4x - X + X, 2 3x, + 2x, + x, + 2x, =5 -3x, - 8x; + 2x - 2x, =-4 X- 6x, + 3x, 1 5. Forward elimination changes Ax = b to a row reduced Rx = d: the general solution is x=0+s1+to What is the 3 x 3 reduced row echelon matrix R and what is d? Find the conditions on a, b, and e so that the following linear system of equations have a solution (7-8): 6. -2x +y +z= a x- 2y +z = x+y-3c O D 630 PM 11/17/2021
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