Exercise · ZW-CRAMERS-RULE-005 · ★☆☆ Basic
In Cramer's rule, to compute \(x_i\) the matrix \(A_i\) is formed from \(A\) by:
Choose one option.
Show answer
- B. replacing column \(i\) with the vector \(\mathbf{b}\)
Explanation
\(A_i\) is \(A\) with its column \(i\) replaced by \(\mathbf{b}\), and \(x_i=\det A_i/\det A\). Changing a row instead of the column gives a different result.
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
- ZW-CRAMERS-RULE-001 Use Cramer's rule to find x in begincases2x+y=7\\ x-y=-1endcases.
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- ZW-CRAMERS-RULE-003 Solve for y with Cramer's rule: begincasesx+2y=8\\ 3x-y=3endcases.
- ZW-CRAMERS-RULE-004 For [1 1 1; 0 2 1; 1 0 3][x; y; z]=[6; 7; 10], use Cramer's rule to find z.
- ZW-CRAMERS-RULE-006 For begincases2x+4y=6\\ x+2y=3endcases, what do you conclude when trying Cramer's rule?
- ZW-CRAMERS-RULE-007 For which values of k does begincaseskx+2y=3\\ 2x+ky=1endcases have a unique solution?
- ZW-CRAMERS-RULE-008 If det A=4 and the determinant of the matrix obtained by replacing column 1 with b is -8, what is x…
- ZW-CRAMERS-RULE-009 Solving a 4×4 system with a unique solution using Cramer's rule requires computing at least: