grandes-ecoles 2025 Q15

grandes-ecoles · France · mines-ponts-maths2__psi Matrices Linear System and Inverse Existence

Prove that the system $V A = B$ admits a unique solution $A \in \mathbf { R } ^ { N }$.
Here $V$ is the matrix from question 14, with entries $V_{k,n} = \lambda_n^{k-1}$ for $k = 1,\ldots,N$ and $n = 1,\ldots,N$, and the $\lambda_n$ are strictly increasing real numbers.

Prove that the system $V A = B$ admits a unique solution $A \in \mathbf { R } ^ { N }$.

Here $V$ is the matrix from question 14, with entries $V_{k,n} = \lambda_n^{k-1}$ for $k = 1,\ldots,N$ and $n = 1,\ldots,N$, and the $\lambda_n$ are strictly increasing real numbers.

Paper Questions

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