a) A matrix A is singular. Find x and state the matrix A. b) Two shopkeepers, Juma and Wanjiku bought some…

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a) A matrix A is singular. Find x and state the matrix A. b) Two shopkeepers, Juma and Wanjiku bought some items from a wholesale... The number of items bought by Juma and Wanjiku using a 2x3 matrix. The prices of the items bought using 3x1 matrix.

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Hapa kuna suluhisho la swali lako: 20. a) Matrix A ni singular. Tafuta x na ueleze matrix A. Matrix A imetolewa kama: A = x & x−1 2 & 4 Matrix ni singular ikiwa determinant yake ni sifuri. Determinant ya matrix 2 × 2, a & b c & d , ni ad − bc. Step 1: Kokotoa determinant ya matrix A. det(A) = (x)(4) − (x−1)(2); det(A) = 4x − (2x − 2); det(A) = 4x − 2x + 2; det(A) = 2x + 2 Step 2: Weka determinant sawa na sifuri na utatue kwa x. 2x + 2 = 0; 2x = −2; x = (−2)/(2); x = −1 Step 3: Eleza matrix A kwa kutumia thamani ya x uliyopata. Badilisha x = −1 kwenye matrix A: A = −1 & (−1)−1 2 & 4 A = −1 & −2 2 & 4 b) Wafanyabiashara wawili, Juma na Wanjiku walinunua bidhaa kutoka kwa muuzaji wa jumla. i) Idadi ya bidhaa zilizonunuliwa na Juma na Wanjiku kwa kutumia matrix ya 2 × 3. Juma alinunua mikate 18, pakiti 40 za maziwa, na sabuni 5. Wanjiku alinunua mikate 15, pakiti 30 za maziwa, na sabuni 6. Matrix ya 2 × 3 (safu 2, nguzo 3) itawakilisha wanunuzi (Juma, Wanjiku) kama safu na bidhaa (mikate, maziwa, sabuni) kama nguzo. Idadi ya bidhaa = 18 & 40 & 5 15 & 30 & 6 ii) Bei za bidhaa zilizonunuliwa kwa kutumia matrix ya 3 × 1. Bei ya mkate ni Ksh. 45. Bei ya pakiti ya maziwa ni Ksh. 50. Bei ya sabuni ni Ksh. 150. Matrix ya 3 × 1 (safu 3, nguzo 1) itawakilisha bei za bidhaa. Bei za bidhaa = 45 50 150 iii) Jumla ya gharama iliyolipwa na kila mfanyabiashara. Ili kupata jumla ya gharama iliyolipwa na kila mfanyabiashara, tunazidisha matrix ya idadi ya bidhaa na matrix ya bei. Step 1: Zidisha matrix ya idadi ya bidhaa na matrix ya bei. Gharama = 18 & 40 & 5 15 & 30 & 6 45 50 150 Step 2: Kokotoa bidhaa ya matrix. Kwa Juma (safu ya kwanza): (18 × 45) + (40 × 50) + (5 × 150) = 810 + 2000 + 750; = 3560 Kwa Wanjiku (safu ya pili): (15 × 45) + (30 × 50) + (6 × 150) = 675 + 1500 + 900; = 3075 Step 3: Andika matokeo kama matrix. Gharama = 3560 3075 Hivyo, Juma alilipa Ksh. 3560 na Wanjiku alilipa Ksh. 3075.

A) A matrix A is singular. Find x and state the matrix A. b) Two shopkeepers, Juma and Wanjiku bought some items from a wholesale... The number of items bought by Juma and Wanjiku using a 2x3 matrix. The prices of the items bought using 3x1 matrix.

Answers

Step-by-step solution

Part b(i)

Part b(ii)
$\begin{bmatrix} 45 \\ 50 \\ 150 \end{bmatrix}$

Part b(iii)· 3 steps
$\begin{bmatrix} 3560 \\ 3075 \end{bmatrix}$

Zidisha matrix ya idadi ya bidhaa na matrix ya bei.

Kokotoa bidhaa ya matrix.

Andika matokeo kama matrix.

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