B05. 136.130: Test #1 Solutions

1. (a) Use elementary row operations to transform the matrix into a matrix in Reduced Row-Echelon Form. Show your work and clearly indicate what you do.

(b) Use elementary row operations to transform the matrix into a matrix in Row-Echelon Form. Show your work and clearly indicate what you do.

Solution. (a)

(b) .

2. Solve the following system. Show your work.

Solution. The augmented matrix is . We start row-reducing: . We see that the equation corresponding to the second row is . Since this could never be satisfied, the system is inconsistent (no solutions).

3. Given , , compute, if possible:

(a)

(b) is not doable since the number of columns of A (=3) is not equal to the number of row in B (=2).

(c) By a formula given in the class we find . So,