Exercise · ZW-CRAMERS-RULE-009 · ★★★ Advanced
Solving a \(4\times4\) system with a unique solution using Cramer's rule requires computing at least:
Choose one option.
Show answer
- C. 5 determinants of order 4
Explanation
You need \(\det A\) and one \(\det A_i\) per unknown: \(1+4=5\) determinants of order 4. That is why Cramer's rule is impractical for large \(n\) compared with Gaussian elimination.
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.
- ZW-CRAMERS-RULE-002 Cramer's rule for a system Ax=b with square A can be applied when:
- 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-005 In Cramer's rule, to compute x_i the matrix A_i is formed from A by:
- 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…