MTH2: MATRICES

This unit is about Addition, multiplication and identity matrices.

MATRICES

A matrix is an ordered rectangular array containing number or letters. Each entry in a matrix is a called an element. Each element has a particular position in raw and a column in a matrix.

Brackets are drawn around the whole array to show that we are treating it as a single matrix.

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  1. A firm sells a number of kits for the amateur radio construction. They sell a kit called beginner’s box. With 3 transistors, 2 coils, 1 speaker, 7 resistors, and 5 capacitors; another straight eight has 8 transistors, 6 coils, 2 speakers, 25 resistors and 24 capacitors while the super six has 6 transistors, 8 coils, 1 speaker , a 23resitors and 16capacitors. Tabulate this information in a 3 x 5 matrix

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A VIDEO ABOUT THE INTRODUCTION TO MATRICES

Exercise

  1. Asha, Koki and Predence decide to make their own dresses for a art. Asha’s paten needs 4.5m of silk, 4m of bindings, a 35cm zip fastener and 3 buttons. Koki’s has a separate jacket; her dress and jacket need 1.5m of silk, 5m of nylon, 1.5m of binding, a 40cm zip-fastener and no buttons. Prudence for a shift needs 2.5m of silk, 2m of binding, but no zip fastener or button. State requirements in matrix form.

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Matrix addition:

Two matrices can be added if they have same order.

Example;

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Combining rows and columns

  1. Work out where possible, the following matrix products:

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  1. b) The shopkeeper orders 2 small 10 medium and 30 large packets. Write this information as a row matrix.

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  1. d) How much did the order cost

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  1. A dress maker buys 36 blue, 30 green and 54 white buttons. The blue cost 20ct each, the green 30ct each and the white buttons 10ct each. Use row and column matrices to work out the total cost of the button.

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Matrix Multiplication

Two matrices are compatible 4 multiplications if and only if the number of columns in the left head matrix is equal to the number of raws in the hand matrix. If A and B are matrices then

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The following table shows how many bags of rice, maize and beans that was bought by for different skuls A, B, C and D from a whole seller.

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If the cost per bag of rice, maize and beans were Ksh. 250, Kjsh 100 and Ksh 60 respectively

Find how much each school spent?

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A VIDEO ABOUT MULTIPLICATION OF MATRICES

For A cost will 1490 Ksh

For B   cost will be Ksh 3250

For C cost will be Ksh 2590

For D cost will be Ksh 3870

Exercise

  1. A factory produces three types of portable radio sets called Pocket, Hand and super. A pocket set contains I transistor (T), 10 resistors (R) and 5 capacitors ©.

A hand set contains 2, 18R and 7C. A super set contains3T, 24R and 10C. Arrange this information in matrix form.

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If the factory’s monthly output is 100 pockets, 200 hand and 80 super set. Find its monthly requirements of transistors, resistors and capacitors.

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Total cost 10sh, R sh 5 and C sh 20. Find the matrix multiplication, the cost of these components

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The identity matrix

Is a matrix such that when you multiply it with another matrix whether on the left or right hand side, you get that matrix.

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The inverse of a matrix

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A matrix which has no inverse is called a singular matrix

Its determinant is equal to zero.

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Hence write down the relationship between (ABC)-1 and A-1, B-1 and C-1.

  1. c) A company making soft drinks has three factories. P, Q and R each of which can produce 3 types of drinks; orange, cola and lemonade each types is bottled in three sizes, large, mini and standard.

The quality of soda bottled each day at the three factories and the proportion of each type in the various bottle sizes is shown in the table below;

Crates of Soda in thousands

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Find the amount of Soda (in thousands of crates) bottled at each factory in each of the three bottle sizes.

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ASSIGNMENT : MATRICES ASSIGNMENT MARKS : 30  DURATION : 3 hours

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