Exercise · ZW-CRAMERS-RULE-004 · ★★☆ Intermediate
For \(\begin{pmatrix}1&1&1\\0&2&1\\1&0&3\end{pmatrix}\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}6\\7\\10\end{pmatrix}\), use Cramer's rule to find \(z\).
Choose one option.
A \(z=15\) B \(z=2\) C \(z=5\) D \(z=3\) Show answer ← Back to the question
Explanation \(\det A=5\). Replacing the third column by \(\mathbf{b}\) gives a determinant of \(15\), so \(z=15/5=3\). The value \(15\) is only the numerator.
Cramer's rule gives the unique solution of a square system, whose coefficient matrix \(A\) has nonzero determinant , as a quotient of determinants.
\[x_i=\frac{\det A_i}{\det A}\]
More practice problems: cramer's rule