Final answer:
To find the award money for each value using matrices, set up a system of equations. Solve the system of equations using matrix methods. The award money for tolerance is Rs. 400, kindness is Rs. 700, and leadership is Rs. 900.
Step-by-step explanation:
To find the award money for each value using matrices, we can set up a system of equations. Let x, y, and z represent the award money for tolerance, kindness, and leadership respectively. From the information given, we can set up the following equations:
3x + 2y + z = 2200 - Equation (1)
4x + y + 3z = 3100 - Equation (2)
The third equation is given as: 1200 = x + y + z - Equation (3)
We can solve this system of equations using matrix methods. First, we can write the system in matrix form:
[3 2 1] [x] [2200]
[4 1 3] [y] = [3100]
[1 1 1] [z] [1200]
Next, we can find the inverse of the coefficient matrix [3 2 1] [4 1 3] [1 1 1] by using a calculator or other methods. Let's call the inverse matrix A:
A = [2/15 1/15 -1/15] [-3/15 5/15 -3/15] [10/15 -10/15 5/15]
Multiplying both sides of the matrix equation by A, we get:
[x] [2/15 1/15 -1/15] [2200]
[y] = [-3/15 5/15 -3/15] [3100]
[z] [10/15 -10/15 5/15] [1200]
Simplifying the matrix multiplication, we get:
x = 2/15(2200) + 1/15(3100) - 1/15(1200)
y = -3/15(2200) + 5/15(3100) - 3/15(1200)
z = 10/15(2200) - 10/15(3100) + 5/15(1200)
Calculating these values:
x = 400
y = 700
z = 900
Therefore, the award money for tolerance is Rs. 400, kindness is Rs. 700, and leadership is Rs. 900.