





Ex 4.6
Ex 4.6, 2 Deleted for CBSE Board 2022 Exams
Ex 4.6, 3 Important Deleted for CBSE Board 2022 Exams
Ex 4.6, 4 Deleted for CBSE Board 2022 Exams
Ex 4.6, 5 Important Deleted for CBSE Board 2022 Exams
Ex 4.6, 6 Deleted for CBSE Board 2022 Exams
Ex 4.6, 7
Ex 4.6, 8
Ex 4.6, 9
Ex 4.6, 10 Important
Ex 4.6, 11
Ex 4.6, 12
Ex 4.6, 13 Important
Ex 4.6, 14 Important
Ex 4.6, 15 Important
Ex 4.6, 16 Important You are here
Ex 4.6, 16 The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix methodLet the cost of onion, wheat & rice per kg be x, y, z respectively. Given, Cost of 4 kg onion, 3 kg wheat & 2 kg rice is Rs 60. 4x + 3y + 2z = 60 Cost of 2 kg onion, 4 kg wheat & 6 kg rice is Rs 90. 2x + 4y + 6z = 90 Cost of 6 kg onion, 2 kg wheat & 3 kg Rice is Rs 70 6x + 2y + 3z = 70 So the system of equation is 4x + 3y + 2z = 60 x + 2y + 3z = 45 6x + 2y + 3z = 70 Writing equation as AX = B [■8(4&3&2@1&2&3@6&2&3)][■8(𝑥@𝑦@𝑧)] = [■8(60@45@70)] Hence A = [■8(4&3&2@1&2&3@6&2&3)], X = [■8(𝑥@𝑦@𝑧)] & B = [■8(60@45@70)] Calculating |A| |𝐴| = [■8(4&3&2@1&2&3@6&2&3)] = 4 (6 − 6) − 1(9 − 4) + 6 (9 − 4) = 4 (0) −1 (5) + 6 (5) = −5 + 30 = 25 So, |A|≠ 0 ∴ The system of equation is consistent & has a unique solution Now, AX = B X = A-1 B Calculating A-1 Now, A-1 = 1/(|A|) adj (A) adj A = [■8(A11&A12&A13@A21&A22&A23@A31&A32&A33)]^′ = [■8(A11&A21&A31@A12&A22&A32@A13&A23&A33)] A = [■8(4&3&2@1&2&3@6&2&3)] Now, 𝐴11 = 2 × 3 −2 × 3 = 6 − 6 = 0 𝐴12 = −[3 × 1−6 × 3] = −[3−18] = −(−15) = 15 𝐴13 = 1 × 2 − 6 × 2 = 2 − 12 = −10 𝐴21 = −[3 × 3−2 × 2 ] = − [9−4] = −5 𝐴22 = 4 × 3 − 6 × 2 = 12 − 12 = 0 𝐴23 = − [2 × 1−6 × 2] = −[2−12] = − (−10) = 10 𝐴31 = 3 × 3 − 2 × 2 = 9 − 4 = 5 𝐴32 = −[4 × 3−2 × 1] = [12−2]=−10 𝐴33 = 4 × 2 − 3 × 1 = 8 − 3 = 5 Hence, adj (A) = [■8(0&−5&5@15&0&−10@−10&10&5)] Now, A−1 = 1/|𝐴| adj (A) A−1 = 1/25 [■8(0&−5&5@15&0&−10@−10&10&5)] A−1 = 1/5 [■8(0&−1&1@3&0&−2@−2&2&1)] Now, X = A−1 B [■8(𝑥@𝑦@𝑧)] = 1/5 [−■8(0&−1&1@3&0&−2@−2&2&1)] [■8(60@45@70)] [■8(𝑥@𝑦@𝑧)] = 1/5 [█(−0−45+70@180+0−140@−120+90+70)] = 1/5 [■8(25@40@40)] [■8(𝑥@𝑦@𝑧)] = [■8(5@8@8)] ∴ x = 5, y = 8, z = 8 Cost of onion, wheat & rice per kg is Rs 5, Rs 8 & Rs 8 Respectively.