Is this a basis for the 3D space?

[-1] [1] [1]

[2] [2] [6]

[1] [2] [5]

Is this a basis for the 3D space?

[-1] [1] [1]

[2] [2] [6]

[1] [2] [5]

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How would you answer that question? In order for it to be a basis, it must be non-singular, right? How can you figure that out?

By calculating the determinant of the matrix formed by these vectors. The determinant is 4. However, this set of vectors is not a basis as per the answer to the quiz. Am I doing right?

Hmmm, no, my calculation of the determinant there is 0, which would mean it is singular and thus not a basis.

I got the determinant 0 when I treated these vectors as column vectors. Do we have to treat these vectors as column vectors always?

If you transpose the matrix, the determinant is still zero, right?