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13-(3/2x)=37
3/2x=24
1.5x=24
x=16
<h2>
Answer:</h2>
The values of x for which the given vectors are basis for R³ is:

<h2>
Step-by-step explanation:</h2>
We know that for a set of vectors are linearly independent if the matrix formed by these set of vectors is non-singular i.e. the determinant of the matrix formed by these vectors is non-zero.
We are given three vectors as:
(-1,0,-1), (2,1,2), (1,1, x)
The matrix formed by these vectors is:
![\left[\begin{array}{ccc}-1&2&1\\0&1&1\\-1&2&x\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%262%261%5C%5C0%261%261%5C%5C-1%262%26x%5Cend%7Barray%7D%5Cright%5D)
Now, the determinant of this matrix is:

Hence,

Answer:
x1 y1 x2 y2
(2 5) (-1 -4)
slope m = (y2-y1)/(x2-x1)
( -4 -5 )/( -1 -2 )
( -1/ -1 )
m= -1/-1
Step-by-step explanation:
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