A2 = [1 2 3; 4 5 6; 7 8 9; 3 2 4; 6 5 4; 9 8 7]
b2 = [1 1 1 1 1 1]′

(a) find a basis for the row space of a2.
(b) how many solutions does a2 ?

Remember, a basis for the row space of a matrix A is the set of rows different of zero of the echelon form of A.

We need to find the echelon form of the matrix augmented matrix of the system A2x=b2

We apply row operations:

1.

We obtain the matrix

2.

We obtain the matrix

3.

we exchange rows three and four of the previous matrix and obtain the echelon form of the augmented matrix.

Since the only nonzero rows of the augmented matrix of the coefficient matrix are the first three, then the set

is a basis for Row (A2)

Now, observe that the last two rows of the echelon form of the augmented matrix have the last coordinate different of zero. Then, the system is inconsistent. This means that the system has no solutions.

14 ft 7 inches

step-by-step explanation:

since each model inch corresponds to 25 real inches, 7 model inches will correspond to

7×25" = 175"

at 12" per foot, that is 14 feet, 7 inches.