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Chapters
Chapter 2: Algebra
Chapter 3: Analytical Geometry
Chapter 4: Trigonometry
Chapter 5: Differential Calculus
Chapter 6: Applications of Differentiation
Chapter 7: Financial Mathematics
Chapter 8: Descriptive Statistics and Probability
Chapter 9: Correlation and Regression Analysis
Chapter 10: Operations Research
Chapter 1: Matrices and Determinants
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 1 Matrices and Determinants Exercise 1.1 [Pages 7  8]
Find the minors and cofactors of all the elements of the following determinant.
`(5,20),(0, 1)`
Find the minors and cofactors of all the elements of the following determinant.
`(1,3,2),(4,1,2),(3,5,2)`
Evaluate `(3,2,4),(2,0,1),(1,2,3)`
Solve: `(2,x,3),(4,1,6),(1,2,7)` = 0
Find AB if A = `[(3,1),(2,1)]` and B = `[(3,0),(1,2)]`
Solve: `(7,4,11),(3,5,x),(x,3,1)` = 0
Evaluate: `(1,a,a^2  bc),(1,b,b^2  ca),(1,c,c^2  ab)`
Prove that `(1/a,bc,b+c),(1/b,ca,c+a),(1/c,ab,a+b)` = 0
Prove that `(a^2,ab,ac),(ab,b^2,bc),(ac,bc,c^2) = 4a^2b^2c^2`
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 1 Matrices and Determinants Exercise 1.2 [Page 12]
Find the adjoint of the matrix A = `[(2,3),(1,4)]`
If A = `[(1,3,3),(1,4,3),(1,3,4)]` then verify that A(adj A) = A I and also find A^{1}.
Find the inverse of the following matrix:
`[(1,1),(2,3)]`
Find the inverse of the following matrix:
`[(3,1),(1,3)]`
Find the inverse of the following matrix:
`[(1,2,3),(0,2,4),(0,0,5)]`
Find the inverse of the following matrix:
`[(3,5,4),(2,3,1),(1,4,6)]`
If A = `[(2,3),(1,6)]` and B = `[(1,4),(1,2)]`, then verify adj (AB) = (adj B)(adj A)
If A = `[(2,2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.
If A = `[(1,2,2),(4,3,4),(4,4,5)]` then, show that the inverse of A is A itself.
If A^{1} = `[(1,0,3),(2,1,1),(1,1,1)]` then, find A.
Show that the matrices A = `[(2,2,1),(1,3,1),(1,2,2)]` and B = `[(4/5,(2)/5,(1)/5),((1)/5,3/5,(1)/5),((1)/5,(2)/5,4/5)]` are inverses of each other.
If A = `[(3,7),(2,5)]` and B = `[(6,8),(7,9)]`, then verify that (AB)^{1} = B^{1}A^{1}
Find m if the matrix `[(1,1,3),(2,λ,4),(9,7,11)]` has no inverse.
If X = `[(8,1,3),(5,1,2),(10,1,4)]` and Y = `[(2,1,1),(0,2,1),(5,p,q)]` then, find p, q if Y = X^{1}
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 1 Matrices and Determinants Exercise 1.3 [Page 15]
Solve by matrix inversion method:
2x + 3y – 5 = 0; x – 2y + 1 = 0.
Solve by matrix inversion method:
3x – y + 2z = 13; 2x + y – z = 3; x + 3y – 5z =  8
Solve by matrix inversion method:
x – y + 2z = 3; 2x + z = 1; 3x + 2y + z = 4
Solve by matrix inversion method:
2x – z = 0; 5x + y = 4; y + 3z = 5
A sales person Ravi has the following record of sales for the month of January, February and March 2009 for three products A, B and C. He has been paid a commission at fixed rate per unit but at varying rates for products A, B and C.
Months  Sales in units  Commission  
A  B  C  
January  9  10  2  800 
February  15  5  4  900 
March  6  10  3  850 
Find the rate of commission payable on A, B and C per unit sold using matrix inversion method.
The prices of three commodities A, B, and C are ₹ x, y, and z per unit respectively. P purchases 4 units of C and sells 3 units of A and 5 units of B. Q purchases 3 units of B and sells 2 units of A and 1 unit of C. R purchases 1 unit of A and sells 4 units of B and 6 units of C. In the process P, Q and R earn ₹ 6,000, ₹ 5,000 and ₹ 13,000 respectively. By using the matrix inversion method, find the prices per unit of A, B, and C.
The sum of three numbers is 20. If we multiply the first by 2 and add the second number and subtract the third we get 23. If we multiply the first by 3 and add second and third to it, we get 46. By using the matrix inversion method find the numbers.
Weekly expenditure in an office for three weeks is given as follows. Assuming that the salary in all the three weeks of different categories of staff did not vary, calculate the salary for each type of staff, using the matrix inversion method.
Week  Number of employees  Total weekly salary (in ₹) 

A  B  C  
1st week  4  2  3  4900 
2nd week  3  3  2  4500 
3rd week  4  3  4  5800 
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 1 Matrices and Determinants Exercise 1.4 [Pages 19  20]
The technology matrix of an economic system of two industries is `(0.50,0.30),(0.41,0.33)` Test whether the system is viable as per Hawkins Simon conditions.
The technology matrix of an economic system of two industries is `(0.6,0.9),(0.20,0.80)`.
Test whether the system is viable as per HawkinsSimon conditions.
The technology matrix of an economic system of two industries is `(0.50,0.25),(0.40,0.67)`. Test whether the system is viable as per HawkinsSimon conditions.
Two commodities A and B are produced such that 0.4 tonne of A and 0.7 tonne of B are required to produce a tonne of A. Similarly 0.1 tonne of A and 0.7 tonne of B are needed to produce a tonne of B. Write down the technology matrix. If 68 tonnes of A and 10.2 tonnes of B are required, find the gross production of both of them.
Suppose the interindustry flow of the product of two industries are given as under.
Production sector  Consumption sector  Domestic demand  Total output  
X  Y  
X  30  40  50  120 
Y  20  10  30  60 
Determine the technology matrix and test Hawkin’s Simon conditions for the viability of the system. If the domestic demand changes to 80 and 40 units respectively, what should be the gross output of each sector in order to meet the new demands.
You are given the following transaction matrix for a twosector economy.
Sector  Sales  Final demand 
Gross output 

1  2  
1  4  3  13  20 
2  5  4  3  12 
 Write the technology matrix
 Determine the output when the final demand for the output sector 1 alone increases to 23 units.
Suppose the interindustry flow of the product of two sectors X and Y are given as under.
Production Sector  Consumption sector  Domestic demand  Gross output 

X  Y  
X  15  10  10  35 
Y  20  30  15  65 
Find the gross output when the domestic demand changes to 12 for X and 18 for Y.
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 1 Matrices and Determinants Exercise 1.5 [Pages 20  22]
Choose the correct answer
The value of x if `(0,1,0),(x,2,x),(1,3,x)` = 0 is
0, –1
0, 1
–1, 1
–1, –1
The value of `(2x + y,x,y),(2y+z,y,z),(2z+x,z,x)` is
xyz
x + y + z
2x + 2y + 2z
0
The cofactor of –7 in the determinant `(2,3,5),(6,0,4),(1,5,7)` is
18
18
7
7
If `Delta = (1,2,3),(3,1,2),(2,3,1)` then `(3,1,2),(1,2,3),(2,3,1)` is
Δ
Δ
3Δ
3Δ
The value of the determinant `[(a,0,0),(0,b,0),(0,0,c)]^2` is
abc
0
a^{2}b^{2}c^{2}
 abc
If A is square matrix of order 3 then kA is
kA
 kA
k^{3}A
 k^{3}A
adj (AB) is equal to:
adj A adj B
adj A^{T} adj B^{T}
adj B adj A
adj B^{T} adj A^{T}
The inverse matrix of `((4/5,(5)/12),((2)/5,1/2))` is
`7/30 ((1/2,5/12),(2/5,4/5))`
`7/30 ((1/2,(5)/12),((2)/5,1/5))`
`30/7 ((1/2,5/12),(2/5,4/5))`
`30/7 ((1/2,(5)/12),((2)/5,4/5))`
If A = `[(a,b),(c,d)]` such that ad  bc ≠ 0 then A^{1} is
`1/("ad"  "bc") ((d,b),(c,a))`
`1/("ad"  "bc") ((d,b),(c,a))`
`1/("ad"  "bc") ((d,b),(c,a))`
`1/("ad"  "bc") ((d,b),(c,a))`
The number of HawkinsSimon conditions for the viability of an inputoutput analysis is ______.
1
3
4
2
The inventor of inputoutput analysis is ______.
Sir Francis Galton
Fisher
Prof. Wassily W. Leontief
Arthur Caylay
Which of the following matrix has no inverse
`((1,1),(1,4))`
`((2,1),(4,2))`
`((cos a, sin a),(sin a, cos a))`
`((sin a, sin a),(cos a, cos a))`
The inverse matrix of `((3,1),(5,2))` is
`((2,1),(5,3))`
`((2,5),(1,3))`
`((3,1),(5,3))`
`((3,5),(1,2))`
If A = `((1,2),(1,4))` then A(adj A) is
`((4,2),(1,1))`
`((4,2),(1,1))`
`((2,0),(0,2))`
`((0,2),(2,0))`
If A and B nonsingular matrix then, which of the following is incorrect?
A^{2} = I implies A^{1} = A
I^{1} = I
If AX = B then X = B^{1}A
If A is square matrix of order 3 then adj A = A^{2}
The value of `(5,5,5),(4x,4y,4z),(3x,3y,3z)` is
5
4
0
3
If A is an invertible matrix of order 2 then det (A^{1}) be equal
det(A)
`1/(det("A"))`
1
0
If A is 3 × 3 matrix and A = 4 then A^{1} is equal to:
`1/4`
`1/16`
2
4
If A is a square matrix of order 3 and A = 3 then adj A is equal to:
81
27
3
9
The value of `(x,x^2  yz,1),(y,y^2zx,1),(z,z^2xy,1)` is
1
0
1
xyz
If A = `(cos theta,sin theta),(sin theta,cos theta)`, then 2A is equal to
4 cos 2θ
4
2
1
If Δ = `(a_11,a_12,a_13),(a_21,a_22,a_23),(a_31,a_32,a_33)` and A_{ij} is cofactor of a_{ij}, then value of Δ is given by:
a_{11}A_{31} + a_{12}A_{32} + a_{13}A_{33}
a_{11}A_{11} + a_{12}A_{21} + a_{13}A_{31}
a_{21}A_{11} + a_{22}A_{12} + a_{23}A_{13}
a_{11}A_{11} + a_{21}A_{21} + a_{31}A_{31}
If `(x,2),(8,5)` = 0 then the value of x is
`(5)/6`
`5/6`
`(16)/5`
`16/5`
If `(4,3),(3,1)` = 5 then the value of `(20,15),(15,5)` is:
5
125
25
0
If any three rows or columns of a determinant are identical then the value of the determinant is:
0
2
1
3
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 1 Matrices and Determinants Miscellaneous Problems [Pages 22  23]
Solve: `(x,2,1),(2,5,x),(1,2,x)` = 0
Evaluate `(10041,10042,10043),(10045,10046,10047),(10049,10050,10051)`
Without actual expansion show that the value of the determinant `(5,5^2,5^3),(5^2,5^3,5^4),(5^4,5^5,5^6)` is zero.
Show that `(0,ab^2,ac^2),(a^2b,0,bc^2),(a^2c,b^2c,0) = 2a^3b^3c^3`
If A = `(1,1,1),(3,4,7),(1,1,1)` verify that A(adj A) = (adj A)(A) = AI_{3}.
If A = `(3,1,1),(15,6,5),(5,2,2)` then, find the Inverse of A.
If A = `[(1,1),(2,3)]` show that A^{2}  4A + 5I_{2} = 0 and also find A^{1}.
Solve by using matrix inversion method:
x  y + z = 2, 2x  y = 0, 2y  z = 1
The cost of 2 Kg of Wheat and 1 Kg of Sugar is ₹ 70. The cost of 1 Kg of Wheat and 1 Kg of Rice is ₹ 70. The cost of 3 Kg of Wheat, 2 Kg of Sugar and 1 Kg of rice is ₹ 170. Find the cost of per kg each item using the matrix inversion method.
The data are about an economy of two industries A and B. The values are in crores of rupees.
Producer  User  Final demand  Total outout  
A  B  
A  50  75  75  200 
B  100  50  50  200 
Find the output when the final demand changes to 300 for A and 600 for B.
Chapter 1: Matrices and Determinants
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 1  Matrices and Determinants
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Concepts covered in Class 11th Business Mathematics and Statistics Answers Guide chapter 1 Matrices and Determinants are Determinants, Input–Output Analysis, Inverse of Matrix.
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