Use Gaussian elimination to find the complete solution to the system of equations, or show that none exists. { x + 3y - 2z - w = 8 4x + y + 4z + 5w = 4 -3x - y + z - 4w = -12 x - y - 3z - 3w = -2 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution set is {( , , , )}. (Simplify your answers.) B. There are infinitely many solutions. The solution set is {( , , , w)}, where w is any real number. (Simplify your answers. Type expressions using w as the variable. Use integers or fractions for any numbers in the expression.)
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First, we write the system of equations in augmented matrix form: ``` [ 1 3 -2 -1 | 8 ] [ 4 1 4 5 | 4 ] [-3 -1 1 -4 | -12] [ 1 -1 -3 -3 | -2 ] ``` Show more…
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