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Matrices

Short Answer Type

161. Three shopkeepers A, B and C go to a store to buy stationery. A purchase 12 dozen note-books, 5 dozen pens and 6 dozen pencils. B purchase 10 dozen note-books, 6 dozen pens and 7 dozen pencils. C purchase 11 dozen note-books, 13 dozen pens and 8 dozen pencils. A note book costs 40 paise, a pen costs Rs. 1-25 and a pencil costs 35 paise. Use matrix multiplication to calculate each individual’s bill.

straight A space purchases space 144 space note minus books comma space 60 space pens comma space 72 space pencils straight B space purchases space 120 space note minus books comma space 72 space pens comma space 84 space pencils. straight C space purchases space 132 space note minus books comma space 156 space pens comma space 96 space pencils. Let space space be space the space matrix space of space purchases. straight D equals space open square brackets table row 140 60 72 row 120 72 84 row 132 156 96 end table close square brackets Let space straight E space be space the space price space matrix. therefore space straight E equals space open square brackets table row cell 0.40 end cell row cell 1.25 end cell row cell 0.35 end cell end table close square brackets therefore DE equals space space open square brackets table row 140 60 72 row 120 72 84 row 132 156 96 end table close square brackets space space open square brackets table row cell 0.40 end cell row cell 1.25 end cell row cell 0.35 end cell end table close square brackets space space space space space space space space space space space equals open square brackets table row cell 57.60 plus 75.00 plus 25.20 end cell row cell 48.00 plus 90.00 plus 29.40 end cell row cell 52.80 plus 195.00 plus 33.60 end cell end table close square brackets space equals space open square brackets table row cell 157.40 end cell row cell 157.80 end cell row cell 281.40 end cell end table close square brackets bill space of space straight A comma space straight B comma space straight C space are space Rs. space 157.80 comma space Rs. space 167.40 space and space Rs. space 281.40 space respectively.

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162.

In space straight a space legislative space assembly space election comma space straight a space political space group space hired space straight a space public space relations space straight f space straight m. space to space promote space its space candidate space in space three space ways space colon space telephone comma space house space calls comma space and space letters. space The space cost space per space contact space left parenthesis in space paise right parenthesis space is space given space in space matrix space straight A space as cost space per space contact straight A equals space open square brackets table row 40 row 100 row 50 end table close square brackets space telephone comma space houseecall comma space letter The space number space of space contacts space of space each space type space made space in space two space cities space straight X space and space straight Y space is space given space by comma straight B equals space open square brackets table row 1000 500 5000 row 3000 1000 10000 end table close square brackets Find space the space total space amount space spent space by space the space group space in space the space two space cities space straight X space and space straight Y.

72 Views

Long Answer Type

163.

. Below is given the network of bus routes connecting the different bus stands of two cities X and Y :

(a) Find the network may ices connecting the cities :

(i) X to Y (ii) Y to X

(b)What is the relation between the far network matrices obtained in (a) above ?

77 Views

Short Answer Type

164. A trust fund has Rs. 30, 000 that, must be invested in two different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs. 30,000 among the two types of bonds. If the trust fund must obtain an annual total interest of:
(a) Rs. 1800 (b) Rs. 2000

148 Views

165. The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs. 80, Rs. 60 and Rs. 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.

99 Views

166. A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below :
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.

95 Views

Long Answer Type

167. 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.
(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.

84 Views

Short Answer Type

168.

Assume Y, Z, W and P are the matrices of order 3 x k x 2 x p, n x 3 and p x k, respectively.
The restrictions on n, k and p so that PY + WY will be defined are :
(A) k = 3, p = n (B) A:is arbitrary,p = 2
(C) p is arbitrary, k = 3 (D)k = 2, p = 3

82 Views

169.

If space straight A space is space square space matrix space such space that space straight A squared equals space straight A comma space then space left parenthesis straight I space plus space straight A right parenthesis cubed space – space 7 straight A space is space equal space to space left parenthesis straight A right parenthesis space straight A space comma space left parenthesis straight B right parenthesis space straight I – space straight A space left parenthesis straight C right parenthesis space 1 space left parenthesis straight D right parenthesis space 3 straight A

75 Views

170.

$If space straight A equals space open square brackets table row straight alpha cell space space space space space space straight beta end cell row straight gamma cell space space minus straight alpha end cell end table close square brackets space space is space such space that space straight A squared space equals space straight I comma space then left parenthesis straight A right parenthesis space straight l space plus space straight alpha squared space plus space βγ space equals space 0 space left parenthesis straight B right parenthesis space straight l – straight alpha squared plus space βγ space equals space 0 space space left parenthesis straight C right parenthesis space 1 space – straight alpha squared space – space βγ space equals space 0 space left parenthesis straight D right parenthesis space straight l space plus straight alpha squared – space βγ space equals space 0$

73 Views