Subjects linear algebra

Matrix Square Submatrix

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Matrix Square Submatrix


1. The problem states: Make matrix $M$ be a square matrix of $C$ and matrix $N$ a square submatrix of $A$. 2. To clarify, a square matrix is a matrix with the same number of rows and columns. 3. Matrix $M$ is defined as a square matrix composed of elements from matrix $C$. This means $M$ has dimensions $n \times n$ for some integer $n$, and each element of $M$ is taken from $C$. 4. Matrix $N$ is a square submatrix of matrix $A$. A submatrix is formed by selecting certain rows and columns from $A$ to form a smaller matrix. 5. Since $N$ is square, it must have the same number of rows and columns, say $k \times k$, where $k \leq$ the dimension of $A$. 6. In summary, $M$ is a square matrix derived from $C$, and $N$ is a square submatrix extracted from $A$. This completes the explanation of the problem as stated.