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

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3