Exercise · ZW-CRAMERS-RULE-008 · ★☆☆ Basic
If \(\det A=4\) and the determinant of the matrix obtained by replacing column 1 with \(\mathbf{b}\) is \(-8\), what is \(x_1\)?
Choose one option.
Show answer
- A. \(-2\)
Explanation
By Cramer's rule, \(x_1=\det A_1/\det A=-8/4=-2\).
Review the concept: Cramer's rule
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
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