MATH 251 Midterm: MATH 304 TAMU Spring 04 Exam 2f
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[18 points] consider the system of equations w + 2y 3z = 10. 3w 6y + 10z = 33 (a) write down the augmented matrix for this system of equations with the variables ordered w, x, y, z. 0 6 10 (b) carry out on paper, step by step, the row reduction algorithm on the augmented matrix and transform it into reduced row echelon form. Solution: this is fairly straightforward, and you eventually arrive in the form. 3 (c) describe completely the set of solutions of this system of equations. Solution: once we have our equations in reduced row echelon form as in (b), our original system is equivalent to the sytem w = 1 2y x = 4 y z = 3. {( 1 2y, 4 y, y, 3) | y r}. Carry this out on paper, step by step. Solution: you nd the inverse by reducing the matrix [a|i] to the form [i|b].
