Samacheer Kalvi solutions for Business Mathematics and Statistics [English] Class 11 TN Board chapter 1 - Matrices and Determinants [Latest edition]

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`

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^-1A^-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

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.

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.

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 Hawkins-Simon 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 Hawkins-Simon 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 inter-industry flow of the product of two industries are given as under.

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 two-sector economy.

1. Write the technology matrix
2. Determine the output when the final demand for the output sector 1 alone increases to 23 units.

Suppose the inter-industry flow of the product of two sectors X and Y are given as under.

Find the gross output when the domestic demand changes to 12 for X and 18 for Y.

The value of x if `|(0,1,0),(x,2,x),(1,3,x)|` = 0 is

The value of `|(2x + y,x,y),(2y+z,y,z),(2z+x,z,x)|` is

The cofactor of –7 in the determinant `|(2,-3,5),(6,0,4),(1,5,-7)|` is

If `Delta = |(1,2,3),(3,1,2),(2,3,1)|` then `|(3,1,2),(1,2,3),(2,3,1)|` is

The value of the determinant `[(a,0,0),(0,b,0),(0,0,c)]^2` is

If A is square matrix of order 3 then |kA| is

adj (AB) is equal to:

The inverse matrix of `((4/5,(-5)/12),((-2)/5,1/2))` is

If A = `[(a,b),(c,d)]` such that ad - bc ≠ 0 then A^-1 is

The number of Hawkins-Simon conditions for the viability of an input-output analysis is ______.

The inventor of input-output analysis is ______.

Which of the following matrix has no inverse

The inverse matrix of `((3,1),(5,2))` is

If A = `((-1,2),(1,-4))` then A(adj A) is

If A and B non-singular matrix then, which of the following is incorrect?

The value of `|(5,5,5),(4x,4y,4z),(-3x,-3y,-3z)|` is

If A is an invertible matrix of order 2 then det (A^-1) be equal

If A is 3 × 3 matrix and |A| = 4 then |A^-1| is equal to:

If A is a square matrix of order 3 and |A| = 3 then |adj A| is equal to:

The value of `|(x,x^2 - yz,1),(y,y^2-zx,1),(z,z^2-xy,1)|` is

If A = `|(cos theta,sin theta),(-sin theta,cos theta)|`, then |2A| is equal to

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:

If `|(x,2),(8,5)|` = 0 then the value of x is

If `|(4,3),(3,1)|` = -5 then the value of `|(20,15),(15,5)|` is:

If any three rows or columns of a determinant are identical then the value of the determinant is:

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) = |A|I₃.

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 A² - 4A + 5I₂ = 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.

Find the output when the final demand changes to 300 for A and 600 for B.