LECTURE-1

Avinash works as a lecturer and earns Rs. 12000 per month. His wife who is a doctor earns Rs. 15000 per month. Find the following ratios: Avinash’s income to the income of his wife. Avinash’s income to their total income.

Let A= [{:(,1,1,1),(,1,1,1),(,1,1,1):}] , B= [{:(,2,-1,-1),(,-1,2,-1),(,-1,-1,2):}] and C=3A+7B

The roots of the equation |{:(x-1,1,1),(1,x-1,1),(1,1,x-1):}|=0 are

If (1+1/(1!)+(1)/(2!)+......oo) (1-(1)/(1!) +1/(2!) -1/(3!) + ......oo)=

The value of the determinant |(-1,1,1),(1,-1,1),(1,1,-1)| is equal to

If [{:(1, 1), (0,1):}]*[{:(1, 2), (0,1):}]*[{:(1, 3), (0,1):}]cdotcdotcdot[{:(1, n-1), (0,1):}] = [{:(1, 78), (0,1):}] , then the inverse of [{:(1, n), (0,1):}] is

Evaluate: a. (-1) times (-1) times (-1) times (-1) times (-1) times (-1) times (-1) times (-1) (-1) times (-1) times (-1) times (-1) times (-1) times (-1) times (-1) times (-1)times (-1) times (-1) times (-1)

If A=[[1, 1, 1],[ 1, 1, 1],[ 1, 1, 1]] , prove that A^n=[[3^(n-1),3^(n-1),3^(n-1)],[3^(n-1),3^(n-1),3^(n-1)],[3^(n-1),3^(n-1),3^(n-1)]], n in N.

If A=[(1,1,1),(1,1,1),(1,1,1)] then show that A^n=[(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1)),(3^(n-1),3^(n-1),3^(n-1))] .

If [1\ -1\ \ x][[0, 1,-1 ],[2 ,1 ,3],[ 1, 1, 1]][[0 ],[1],[ 1]]=0 , find xdot