Construct a 3 x 3 matrix a, with nonzero entries, and a vector b in r3 such that b is not in the set spanned by the columns of a.

and

Step-by-step explanation:

You can choose a 3x3 matrix whose colums are not linearly independet. (observe that if you choose 3 independet vectors as columns of your matrix, the set spanned by the colums will be and there would not be such b).

Consider the vector and the 3x3 matrix

Then, the set spanned by the columns is

{}

So,

as we wanted.

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

the answer is c)8

step-by-step explanaction: