Advertisements
Advertisements
प्रश्न
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
उत्तर
(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
संबंधित प्रश्न
If A = `[(8, -3)]` and B = `[(4, -5)]`; find A + B
Wherever possible, write the following as a single matrix.
`[(2, 3, 4),(5, 6, 7)] - [(0, 2, 3),(6, -1, 0)]`
Evaluate:
`2[(-1 0)/(2 -3)] +[(3 3)/(5 0)]`
State, with reason, whether the following is true or false. A, B and C are matrices of order 2 × 2.
A + B = B + A
Find the values of x and y, if `|(3"x" - "y"),(5)| = |(7) , ("x + y")|`
Evaluate the following :
`|(1 , 1),(2 , 3)| |(2 , 1),(1 , 4)|`
If P = `|(1 , 2),(2 , 1)|` and Q = `|(2 , 1),(1 , 2)|` find P (QP).
`[(3),(0),(-1)]`
Let `"M" xx [(1, 1),(0, 2)]` = [1 2] where M is a matrix.
- State the order of matrix M
- Find the matrix M
If a matrix A = `[(0, 1),(2, -1)]` and matrix B = `[(3),(1)]`, then which of the following is possible:
