Learn All Concepts of Chapter 3 Class 12 Matrices - FREE. Check - Matrices Class 12 - Full video

Last updated at Jan. 17, 2020 by Teachoo

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Misc 10 A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: Market Products I 10,000 2,000 18,000 II 6,000 20,000 8,000 (a) If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00, respectively. Find the total revenue in each market with the help of matrix algebra. Let the sales of products x , y & z per market be denoted by matrix A A = [■8(10,000&2000&18,000@6,000&20,000&8,000)] Let the unit sale price of products x , y & z per market be denoted by matrix B Let B = [■8( 2.50 @1.50@1.00)] Now, Total Revenue = Total sales × Unit sales price = AB = [■8(10,000&2000&18,000@6,000&20,000&8,000)]_(2×3) [■8(2.50@1.50@1.00)]" " _(3×1) = [■8(10,000(2.50)+2000(1.50)+18,000(1)@6,000(2.50)+20,000(1.50)+8,000(1) )] = [■8(25,000+3,000+18,000@15,000+30,000+8,000)]= [■8(46,000@53,000)] Total Revenue = [■8(46,000@53,000)] Hence, Total revenue of Market I = Rs. 46,000 & Total revenue of Market II = Rs. 53,000 Note: We cannot do BA BA = [■8(2.50@1.50@1.00)]" " _(3×1) [■8(10,000&2000&18,000@6,000&20,000&8,000)]_(2×3) Since, orders does not match, BA is not possible Misc 10 A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: Market Products I 10,000 2,000 18,000 II 6,000 20,000 8,000 (b) If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit. Let the unit cost price of products x , y & z per market be denoted by matrix C Let C = [■8( 2.00 @1.00@0.50)] Now, Total Cost = Total sales × Unit cost price = AC = [■8(10,000&2000&18,000@6,000&20,000&8,000)]_(2×3) [■8(2.00@1.00@0.50)]" " _(3×1) = [■8(10,000(2.00)+2000(1.00)+18,000(0.50)@6,000(2.00)+20,000(1.00)+8,000(0.50) )] = [■8(20,000+2,000+9,000@12,000+20,000+4,000)] = [■8(31,000@36,000)] Now, Profit = Revenue – Cost = [■8(46,000@53,000)] – [■8(31,000@36,000)] = [■8(15,000@17,000)] Thus, Profit = = [■8(15,000@17,000)] Hence, Total profit of Market I = Rs. 15,000 & Total profit of Market II = Rs. 17,000

Statement questions - Multiplication of matrices

Chapter 3 Class 12 Matrices

Concept wise

- Formation and order of matrix
- Types of matrices
- Equal matrices
- Addition/ subtraction of matrices
- Statement questions - Addition/Subtraction of matrices
- Multiplication of matrices
- Statement questions - Multiplication of matrices
- Solving Equation
- Finding unknown - Element
- Finding unknown - Matrice
- Transpose of a matrix
- Symmetric and skew symmetric matrices
- Proof using property of transpose
- Inverse of matrix using elementary transformation
- Proof using mathematical induction

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.