Utilize the Gauss-Jordan elimination method to solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)&nbsp;x+2y+z=−4&nbsp;−2x−3y−z=2&nbsp;4x+8y+4z=−16

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Utilize the Gauss-Jordan elimination method to solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)&amp;nbsp;x+2y+z=−4&amp;nbsp;−2x−3y−z=2&amp;nbsp;4x+8y+4z=−16

seibesitoeu · Accepted Answer

We have given system of equations x + 2y + z = −4 −2x − 3y − z = 24 x + 8y + 4z = −16 The augmented matrix of given system is [121|−4−2−3−1|2484|−16] The pivot element in first row and first column is 1. Now applying the following row transformations on augmented matrix. R2→R2+2R1 R3→R3−4R1 [121|−4011|−6000|0] The pivot element in second row and second coulmn is 1. Apply following transformation on previous matrix. R1→R1−2R2 [10−1|8011|−6000|0] Rewriting the system of equation from this row reduced matrix, x − z=8y + z = −6 The number of equations = 2 Number of variables = 3 Number of variables is greater than number of equations hence given system has infinitely many solutions. Number of free variables = Number of variables - Number of equations = 3 - 2 = 1 Substitute t for z. ⇒x − t=8 and y + t = −6 ⇒x = t + 8 and y = −t −6 Therefore, x = t + 8, y = −t − 6 and z = t. Answer: The given system has infinitely many solutions and the solution set is x = t + 8, y = −t − 6, z = t.

Solve the system of linear equations, using the Gauss-Jordan elimination

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