undefined Solution To solve: The linear system { x + y − z = 9 8 y + 6 z = − 6 − 2 x + 4 y − 6 z = 40 by augmented matrix. The solution of the linear system is x = 1 , y = 3 , z = − 5 _ . The given linear system is { x + y − z = 9 … ( 1 ) 8 y + 6 z = − 6 … ( 2 ) − 2 x + 4 y − 6 z = 40 … ( 3 ) . The augmented matrix of the above linear system is given by, [ 1 1 − 1 9 0 8 6 − 6 − 2 4 − 6 40 ] Apply the row operation to the augmented matrix as follows. [ 1 1 − 1 9 0 8 6 − 6 − 2 4 − 6 40 ] R 3 → R 3 + 2 R 1 ~ [ 1 1 − 1 9 0 8 6 − 6 0 6 − 8 58 ] R 3 → 6 R 2 − 8 R 3 ~ [ 1 1 − 1 9 0 8 6 − 6 0 0 100 − 500 ] From the above, observe that 100 z = − 500 , 8 y + 6 z = − 6 which gives the value of z as, 100 z = − 500 z = − 500 100 z = − 5 Substitute the value of z in the above equation and obtain the value of y . 8 y + 6 z = − 6 8 y + 6 ( − 5 ) = − 6 8 y = − 6 + 30 y = 24 8 y = 3 Substitute the values of y and z in the equation (1) and obtain the value of x . x + y − z = 9 x + 3 − ( − 5 ) = 9 x = 9 − 3 − 5 x = 1 Thus, the solution of the linear system is x = 1 , y = 3 , z = − 5 _ .

10th Edition

ISBN: 9781119455929

Author: Kreyszig

Publisher: WILEY

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‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…

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