<prompt> Kiasi cha parallelepiped kinachozalishwa na beginpmatrix 2 3 4 endpmatrix, beginpmatrix 1 k 2 endpmatrix, na startpmatrix 1 2 k mwishopmatrix ni 15. Tafuta k, ambapo k 0.  <response>: Kiasi cha parallelepiped kinachozalishwa na beginpmatrix 2 3 4 endpmatrix, beginpmatrix 1 k 2 endpmatrix, na startpmatrix 1 2 k endpmatrix imetolewa na thamani kamili ya kibainishi.anzavmatrix 2 1 1 3 k 2 4 2 k endvmatrix.Tunaweza kupanua kibainishi kama ifuatavyo:anzaalignanzavmatrix 2 1 1 3 k 2 4 2 k mwishovmatrix 2 anzavmatrix k 2 2 k mwishovmatrix - anzavmatrix 3 2 4 k mwishovmatrix anzavmatrix 3 k 4 2 mwishovmatrix 2k2 - 4 - 3k - 8 6 - 4k 2k2 - 7k 6.endalignKwa hivyo, ujazo wa parallelepiped ni 2k2 - 7k 6 15. Masuluhisho ya 2k2 - 7k 6 15 ni k -1 na k frac92. Mlinganyo 2k2 - 7k 6 -15 haina suluhu halisi. Tangu k 0, k frac92. 