The first digure below shows the augmented matrixx, A for a nonsquare linear sys

Question

The first digure below shows the augmented matrixx, A for a nonsquare linear system of three equations in foar variables, w, x, y, and z. the second figure shows the reduced row-echelon fomr of matriz A. Complete part a and b.

a.

b.

a. Write the system reproesented by a.

[                    ]

[                   ]

[                   ]

b. Use the reduced row-echelon form a a. to find the system's complete solution. Select the correct choice below and fill in any answer boxes with your choice.

[ ] A. The is one sloution. The solution seit is {([ ], [ ], [ ], [ ])}. (Simplify your answers.)

[ ] B. There are infinitely many solutions. the solution set is {([ ], [ ], y, z)}, where y amd z are any real numbers. (type expessions using y and z as the variables. Use integers or fraction for any numbers in the expressions.

[ ] C. Ther is no solution.

Explanation / Answer

a.

From the given augmented matrix we have the following system of linear equation:-

7w+8x+11y+11z= 3

7w+7x+9y+10z =5

7w+5x+5y+8z = 9

b.

From the last row (3rd row) we have 0=0 which is true hence the system of equation has infinitely many solutions. hence B is correct and the solution set is

{19/7 + (5/7) y - (3/7)z , -2-2y-z , y, z}

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