Determine if b is a linear combination of the vectors formed from the columns of the matrixA=[1 -4 2] B=[3] [ 0 3 5] [-7] [-2 8 -4] [-3]

isn't a linear combination of the vectors formed from the columns of the matrix

Step-by-step explanation:

The question is misspelled. The correct matrix and vector are :

In order to determine if is a linear combination of the vectors formed from the columns of the matrix we write the following linear combination with the columns from :

        (I)

This can be also written as :

Where is the following vector :

The matrix from the system (I) is :

Applying matrix operations to the system matrix we obtain this equivalent matrix :

From the third row we obtain that

Which is an absurd. Therefore the system has no solution and it doesn't exist a linear combination of the vectors formed from the columns of the matrix to obtain the vector .

Finally, isn't a linear combination of the vectors formed from the columns of the matrix

  12 miles per hour

Showing Work :

This is a fraction equal to

30 miles ÷ 2.5 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 2.5

30 miles÷ 2.5

2.5 hours÷ 2.5

=  

12 miles

1 hour

=  

12 miles

hour

= 12 miles per hour