Does $A\in R^{3\times3}$ with first row $\pmatrix {1&2&3} $ exist (?), if...
Does this matrix exist (eigenvalue given)?
0
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$A$ can be inverted and one of its eigenvalues is zero
linear-algebra
matrices
eigenvalues-eigenvectors
determinant
2 Answers
6
If $A$ has an eigenvalue of zero, then it necessarily cannot be inverted (that is, $A$ is singular). So, the answer is no.
4
Nope. A square matrix is invertible iff zero is not one of its eigenvalues, as otherwise its kernel's dimension (the matrix's nullity) is bigger than zero