The reduced row-echelon form of the augmented matrix for a system of linear equations with variables x1,⋯,x4 is given below. Determine the solutions for the system and enter them below. [10−1−5|0013−3|−1] If the system has infinitely many solutions, select "The system has at least one solution". Your answer may use expressions involving the parameters r, s, and t. The system has at least one solution x1=0 x2=0 x3=0 x4=0

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The reduced row-echelon form of the augmented matrix for a system of linear equations with variables x1,⋯,x4 is given below. Determine the solutions for the system and enter them below. [10−1−5|0013−3|−1] If the system has infinitely many solutions, select &quot;The system has at least one solution&quot;. Your answer may use expressions involving the parameters r, s, and t. The system has at least one solution x1=0 x2=0 x3=0 x4=0

Alix Ortiz · Accepted Answer

Step 1 Since rank(augmented matrix) Step 2 Given row-reduced form at augmented matrix [10−1−5|0013−3|−1] So consider system of linear equation with variable x1,x2,x3,and x4. [10−1−5013−3][x1x2x3x4]=[01] System has intinitely many solution as rank of augmented matrix is 2 which is strictly less than number of (4) column x1−x3−5x4=0 x2+3x3−3x4=0 So solution set S={(x1,x2,x3,x4)x1−x3−5x4=0x2+3x3−3xd=0} S={(x1,x2,x3,x4)x1=x3−5x4=0 andx4=13(x2+3x3)} S={(x1,x2,x3,x4)x1=x3−53x2−5x3} S={(x1,x2,x3,x4)3x1=−5x2−12x3} S={(x1,x2,x3,x4)3x1+5x2+12x3=0} then surely x1=0,x2=0,x3=0,x4=0 is one at the solution and called trivial solution.

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