This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Tafuta zao la matriki hizo mbili. Tutaweka matriki ya kwanza kama M_1 na ya pili kama M_2. M_1 = 0 & 1 \\ 2 & p M_2 = -1.5 & -0.5 \\ p & p-2 Zao la matriki M_1 M_2 ni: M_1 M_2 = (0)(-1.5) + (1)(p) & (0)(-0.5) + (1)(p-2) \\ (2)(-1.5) + (p)(p) & (2)(-0.5) + (p)(p-2) M_1 M_2 = 0 + p & 0 + p-2 \\ -3 + p^2 & -1 + p^2 - 2p M_1 M_2 = p & p-2 \\ p^2 - 3 & p^2 - 2p - 1 Step 2: Tafuta kigezo (determinant) cha matriki ya zao. Kwa matriki a & b \\ c & d , kigezo ni ad - bc. Hivyo, kwa matriki yetu p & p-2 \\ p^2 - 3 & p^2 - 2p - 1 : (M_1 M_2) = p(p^2 - 2p - 1) - (p-2)(p^2 - 3) Panua maneno: (M_1 M_2) = (p^3 - 2p^2 - p) - (p(p^2) - p(3) - 2(p^2) - 2(-3)) (M_1 M_2) = (p^3 - 2p^2 - p) - (p^3 - 3p - 2p^2 + 6) Ondoa mabano: (M_1 M_2) = p^3 - 2p^2 - p - p^3 + 3p + 2p^2 - 6 Unganisha vigezo vinavyofanana: (M_1 M_2) = (p^3 - p^3) + (-2p^2 + 2p^2) + (-p + 3p) - 6 (M_1 M_2) = 0 + 0 + 2p - 6 (M_1 M_2) = 2p - 6 Step 3: Linganisha kigezo na sifuri na utafute thamani ya p. Kwa kuwa matriki ni singular, kigezo chake ni sifuri. 2p - 6 = 0 Ongeza 6 pande zote mbili: 2p = 6 Gawanya kwa 2: p = (6)/(2) p = 3 Thamani ya p ni 3. Thamani ya p ni 3. Tuma swali linalofuata 📸