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I am trying to determine if this is linearly independent and I continue to get the wrong answer. I have gotten the determinant to be both $4$ and $2$ although the answer says it should be

$2-2i$ and therefore since it does not equal zero it would be linearly independent. I am not sure where the answer $2-2i$ comes from.

$$\begin{array}{l}1&0&0&1\\0&1&-i&0\\0&1&i&0\\i&0&0&-i\end{array}$$

does anyone know how to do this using coffactors???

Harley McFarlen
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  • You can compute the determinant by reducing the matrix to triangular form, as you would for a real matrix. Is that what you tried to do? – saulspatz Dec 02 '18 at 22:53
  • No I have mostly been taught to do it by cofactor but I am struggling to understand it. Would i need to do the co factor method for each row and column or just one? the instructor is very confusing – Harley McFarlen Dec 02 '18 at 22:55
  • Checking online, I do see that the determinant is 4... hmm – K Split X Dec 02 '18 at 22:57
  • https://www.symbolab.com/solver/matrix-determinant-calculator/%5Cdet%5Cbegin%7Bpmatrix%7D1%260%260%261%5C%5C%200%261%26-i%260%5C%5C%200%261%26i%260%5C%5C%20i%260%260%26-i%5Cend%7Bpmatrix%7D – K Split X Dec 02 '18 at 22:59
  • I get $4$. You only expand by minors along one row or column. – saulspatz Dec 02 '18 at 22:59
  • Yeah... thats why i am so lost, because the text book says its 2-2i and therefore linearly independent – Harley McFarlen Dec 02 '18 at 22:59
  • It is possible that the textbook has made a mistake, and it seems like this is the case here. Regardless, your answer is correct, and I would accept it. – K Split X Dec 02 '18 at 23:00
  • you determine linear independence with the determinant right? – Harley McFarlen Dec 02 '18 at 23:00
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    Your answer is correct. Either the answer in the book is wrong, or you have miscopied the matrix. And yes, as long as the determinant is not zero, the rows and the columns are both linearly independent. – saulspatz Dec 02 '18 at 23:02

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