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 A na B (AB). Tumepewa matriki A = k & 4 \\ 3 & 2 na B = 1 & 2 \\ 3 & 4 . AB = k & 4 \\ 3 & 2 1 & 2 \\ 3 & 4 AB = (k)(1) + (4)(3) & (k)(2) + (4)(4) \\ (3)(1) + (2)(3) & (3)(2) + (2)(4) AB = k + 12 & 2k + 16 \\ 3 + 6 & 6 + 8 AB = k + 12 & 2k + 16 \\ 9 & 14 Step 2: Tafuta kigezo (determinant) cha matriki AB. Kwa matriki a & b \\ c & d , kigezo ni ad - bc. (AB) = (k + 12)(14) - (2k + 16)(9) (AB) = 14k + 168 - (18k + 144) (AB) = 14k + 168 - 18k - 144 (AB) = -4k + 24 Step 3: Linganisha kigezo na 4 na utafute thamani ya k. Tumepewa kuwa (AB) = 4. -4k + 24 = 4 Toa 24 pande zote mbili: -4k = 4 - 24 -4k = -20 Gawanya kwa -4: k = (-20)/(-4) k = 5 Thamani ya k ni 5. Thamani ya k ni 5. 3 done, 2 left today. You're making progress.