Theory question 104
Matrices and DeterminantsSolve: |−2n + 3, n + 1 / 2n, n| = |−2n + 5, 4n / −n + 2, 3n| (determinants written row by row; / separates the rows)
Show the model answer
Model answer
Left: n(−2n + 3) − 2n(n + 1) = −4n² + n.
Right: 3n(−2n + 5) − 4n(−n + 2) = −2n² + 7n.
−4n² + n = −2n² + 7n gives −2n² − 6n = 0, i.e. −2n(n + 3) = 0.
n = 0 or n = −3.
Explanation
Expand each 2 × 2 determinant as ad − bc, then solve the quadratic.