Practice question · Select all that apply
Consider the matrix with rows (1, 2) and (2, 4). Select every TRUE statement about it.
Hints
- Compute the determinant first; everything else follows from it.
- Row 2 is exactly twice row 1.
Show the answer
- B. It is singular
- C. Its rows are proportional
- E. Its determinant is 0
Why
The determinant is 1(4) - 2(2) = 0, so the matrix is singular with no inverse, and its proportional rows are why. With a zero determinant the system Ax = b has either no solution or infinitely many, depending on b, never a unique one.
Practise Matrix Inverses
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