Practice question · Fill in the blanks
Complete the Invertible Matrix Theorem summary.
A square matrix A is ______ if and only if det(A) is ______ and A has ______ rank.
Word bank: invertible · singular · zero · nonzero · full
Hints
- The theorem ties rank, determinant and solvability into one statement.
- Full rank and a nonvanishing determinant say the same thing.
Show the answer
A square matrix A is invertible if and only if det(A) is nonzero and A has full rank.
Why
Full rank, nonzero determinant, and invertibility are all equivalent.
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