query: For what values of $x_1, x_2, x_3, x_4$ is the matrix $A$ invertible?
positive_passages.docid: 52083
positive_passages.text: Vandermonde determinant for order 4
negative_passages.docid: 98323
negative_passages.text: If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
negative_passages.docid: 124734
negative_passages.text: If $A^3=O$ is the matrice $A^2-A+I$ invertible?
negative_passages.docid: 79061
negative_passages.text: show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
negative_passages.docid: 113518
negative_passages.text: Determinant of the inverse matrix
negative_passages.docid: 124942
negative_passages.text: Prove that an upper triangular matrix is invertible if and only if every diagonal entry is non-zero.
negative_passages.docid: 141286
negative_passages.text: When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
negative_passages.docid: 46110
negative_passages.text: how many 2x2 matrices are invertible in mod p
negative_passages.docid: 57296
negative_passages.text: A non-diagonal $4\times4$ matrix such that $A^3=A^2=0$ and its rank is $2$
negative_passages.docid: 42467
negative_passages.text: Inverse of an invertible triangular matrix (either upper or lower) is triangular of the same kind
negative_passages.docid: 52946
negative_passages.text: If $X$ is an orthogonal matrix, why does $X^TX = I$?
negative_passages.docid: 33559
negative_passages.text: Product or sum of invertible matrix give an invertible matrix?
negative_passages.docid: 119052
negative_passages.text: Finding invertible elements in $\mathbb{Z}/m\mathbb{Z}$
negative_passages.docid: 141105
negative_passages.text: Show that there exists a $3 × 3$ invertible matrix $M$ with entries in $\mathbb{Z}/2\mathbb{Z}$ such that $M^7 = I_3$.
negative_passages.docid: 111769
negative_passages.text: Why is inverse of orthogonal matrix is its transpose?
negative_passages.docid: 97781
negative_passages.text: invertible matrices connected or not
negative_passages.docid: 57318
negative_passages.text: Property of the conjugate transpose matrix with inner product