Compute A-2B if A=[3 1; 0 -2] and B=[1 0; 4 1].

Exercise · ZW-MATRIX-007 · ★★☆ Intermediate

Compute \(A-2B\) if \(A=\begin{pmatrix}3&1\\0&-2\end{pmatrix}\) and \(B=\begin{pmatrix}1&0\\4&1\end{pmatrix}\).

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First \(2B=\begin{pmatrix}2&0\\8&2\end{pmatrix}\), then subtract entry by entry: \(A-2B=\begin{pmatrix}1&1\\-8&-4\end{pmatrix}\).

A matrix \(A\) is a rectangular array of numbers arranged in rows and columns; with \(m\) rows and \(n\) columns, it has size \(m\times n\).

\[A=\begin{pmatrix}a_{11}&\cdots&a_{1n}\\ \vdots&\ddots&\vdots\\ a_{m1}&\cdots&a_{mn}\end{pmatrix}\]