Balbharati Maharashtra State Board12th Commerce Maths Solution Book PdfChapter 2 Matrices Ex 2.6 Questions and Answers.
Maharashtra State Board 12th Commerce Maths Solutions Chapter 2 Matrices Ex 2.6
Solution & Step-by-Step Answer:
The given equations can be written in the matrix form as: By equality of matrices, x = 0, y = 1 is the required solution.
(ii) 2x + y = 5, 3x + 5y = -3
Solution:
(iii) 2x – y + z = 1, x + 2y + 3z = 8 and 3x + y – 4z = 1
Solution:
The given equations can be written in the matrix form as:
By equality of matrices,
x = 1, y = 2, z = 1 is the required solution.
(iv) x + y + z = 1, x – y + z = 2 and x + y – z = 3
Solution:
Solution & Step-by-Step Answer:
The given equations can be written in the matrix form as: Hence, x = , y = is the required solution.
(ii) 3x – y = 1, 4x + y = 6.
Solution:
The given equations can be written in the matrix form as:
By equality of matrices,
12x – 4y = 4 …..(1)
7y = 14 …..(2)
From (2), y = 2
Substituting y = 2 in (1), we get
12x – 8 = 4
∴ 12x = 12
∴ x = 1
Hence, x = 1, y = 2 is the required solution.
(iii) x + 2y + z = 8, 2x + 3y – z = 11 and 3x – y – 2z = 5.
Solution:
The given equations can be written in the matrix form as:
By equality of matrices,
x + 2y + z = 8 ……(1)
-y – 3z = -5 …….(2)
16z = 16 ……….(3)
From (3), z = 1
Substituting z = 1 in (2), we get
-y – 3= -5
∴ y = 2
Substituting y = 2, z = 1 in (1), we get
x + 4 + 1 = 8
∴ x = 3
Hence, x = 3, y = 2, z = 1 is the required solution.
(iv) x + y + z = 1, 2x + 3y + 2z = 2 and x + y + 2z = 4.
Solution:
The given equations can be written in the matrix form as:
By equality of matrices,
x + y + z = 1 ……(1)
y = 0
z = 3
Substituting y = 0, z = 3 in (1), we get
x + 0 + 3 = 1
∴ x = -2
Hence, x = -2, y = 0, z = 3 is the required solution.
Solution & Step-by-Step Answer:
Let the cost of each T.V. be ₹ x and each V.C.R. be ₹ y. Then the total cost of 3 T.V. and 2 V.C.R. is ₹ (3x + 2y) which is given to be ₹ 35000. ∴ 3x + 2y = 35000 The shopkeeper wants a profit of ₹ 1000 per T.V. and ₹ 500 per V.C.R. The selling price of each T.V. is ₹ (x + 1000) and of each V.C.R. is ₹ (y + 500). ∴ selling price of 2 T.V. and 1 V.C.R is ₹ [2(x + 1000) + (y + 500)] which is given to be ₹ 21500. ∴ 2(x + 1000) + (y + 500) = 21500 ∴ 2x + 2000 + y + 500 = 21500 ∴ 2x + y = 19000 Hence, the system of linear equations is 3x + 2y = 35000 2x + y = 19000 The equations can be written in matrix form as: By equality of matrices, -x = -3000 …….(1) 2x + y = 19000 ……….(2) From (1), x = 3000 Substituting x = 3000 in (2), we get 2(3000) + y = 19000 ∴ y = 19000 – 6000 = 13000 Hence, the cost price of one T.V. is ₹ 3000 and of one V.C.R. is ₹ 13000 and the selling price of one T.V. is ₹ 4000 and of one V.C.R. is ₹ 13500.
Solution & Step-by-Step Answer:
Let the cost of 1 Economic book, 1 Cooperation book and 1 Account book be ₹ x, ₹ y and ₹ z respectively. Then, from the given information x + y + z = 420 x + 2y + z = 480 x + 3y + 2z = 600 These equations can be written in matrix form as: By equality of matrices, x + y + z = 420 …….(1) y = 60 2y + z = 180 ………(2) Substituting y = 60 in (2), we get 2(60) + z = 180 ∴ z = 180 – 120 = 60 Substituting y = 60, z = 60 in (1), we get x + 60 + 60 = 420 ∴ x = 420 – 120 = 300 Hence, the cost of each Economic book is ₹ 300, each Cooperation book is ₹ 60 and each Account book is ₹ 60.
