Advertisements
Advertisements
Question
Let A = `|(3 , 2),(0 ,5)|` and B = `|(1 ,0),(1 ,2)|` , find (i) (A + B)(A - B) (ii) A2 - B2 . Is (i) equal to (ii) ?
Advertisements
Solution
(i) A = `|(3 , 2),(0 ,5)|_(2 xx 2)` , B = `|(1 ,0),(1 ,2)|_(2 xx 2)`
A + B = `|(3+1 , 2+0),(0+1 ,5 +2)| = |(4,2),(1,7)|_(2xx2)`
A - B = `|(3-1 , 2-0),(0-1 , 5-2)| = |(2 , 2),(-1,3)|_(2 xx 2)`
(A + B)(A - B) = `|(4 , 2),(1 , 7)| |(2 , 2),(-1,3)|`
`=|(8 - 2 , 8+6),(2 - 7 , 2+21)| = |(6,14),(-5,23)|` .......(1)
(ii) A2
= `|(3,2),(0,5)| |(3,2),(0,5)| = |(9+0 , 6+10),(0 + 0 , 0+25)| = |(9,16),(0,25)|_(2 xx 2)`
B2 = `|(1 ,0),(1 ,2)| |(1 ,0),(1 ,2)| = |(1+0 , 0 + 0),(1 + 2 , 0 + 4)| = |(1 , 0),(3 , 4)|_(2 xx 2)`
A2 - B2 = `|(9,16),(0,25)| - |(1 , 0),(3 , 4)| = |(8,16),(-3 ,21)|_(2 xx 2)` ..............(2)
from (1) and (2)
(i) ≠ (ii)
APPEARS IN
RELATED QUESTIONS
State, whether the following statement is true or false. If false, give a reason.
Transpose of a square matrix is a square matrix.
Solve for a, b and c; if `[(-4, a + 5),(3, 2)] = [(b + 4, 2),(3, c- 1)]`
Find x and y from the given equations:
`[(-8, x)] + [(y, -2)] = [(-3, 2)]`
Classify the following matrix :
`[(7, 0)]`
Classify the following matrix :
`|(800),(521)|`
Find the values of a, b, c and d, if `|("a + 3b", 3"c" + "d"),(2"a" - "b" , "c" - 2"d")| = |(5 , 8),(3 , 5)|`
If A = `|("p","q"),(8,5)|` , B = `|(3"p",5"q"),(2"q" , 7)|` and if A + B = `|(12,6),(2"r" , 3"s")|` , find the values of p,q,r and s.
Evaluate the following :
`|(0 , 1),(-1 , 2),(-2 , 0)| |(0 , -4 , 0),(3 , 0 , -1)|`
If A = `[(5, -2),(7, -0)]` and B = `[(8),(3)]`, then which of the following is not possible?
If `M xx [(3, 2),(-1, 0)] = [(3, -1)]`, the order of matrix M is ______.
