Advertisements
Advertisements
प्रश्न
If X = `|(1 , -2),(1 , 3)|` , Y = `|(-3 , 0),(4 , 1)|` and Z = `|(5 , -1),(3 , 2)|` , prove that X (Y + Z) = XY + XZ
उत्तर
X = `|(1 , -2),(1 , 3)|_(2 xx 2)` Y = `|(-3 , 0),(4 , 1)|_(2 xx 2)` Z = `|(5 , -1),(3 , 2)|_(2 xx 2)`
(Y + Z) = `|(-3 , 0),(4 , 1)| + |(5 , -1),(3 , 2)| = |(2 , -1),(7 , 3)|_(2 xx 2)`
X (Y + Z) = `|(1 , -2),(1 , 3)| |(2 , -1),(7 , 3)|`
`= |(2 - 14 , -1-6),(2 + 21 , -1+9)|`
X (Y + Z) = `|(-12 , -7),(23 , 8)|_(2 xx 2)` ........(1)
XY = `|(1 , -2),(1 , 3)| |(-3 , 0),(4 , 1)|`
=`|(-3-8 , 0-2),(-3+12 , 0 + 3)|`
`= |(-11 , -2),(9 , 3)|_(2 xx 2)`
XZ = `|(1 , -2),(1 , 3)| |(5 , -1),(3 , 2)|`
`= |(5 - 6 , -1-4 ),(5 + 9 , -1 + 6)|`
`= |(-1 , -5),(14 , 5)|_(2 xx 2)`
XY + XZ = `|(-11 , -2),(9 , 3)| + |(-1 , -5),(14 , 5)| = |(-12 , -7),(23 , 8)|_(2 xx 2)` ......(2)
from (1) and (2) X(Y + Z) = XY + YZ
APPEARS IN
संबंधित प्रश्न
Write the additive inverse of matrices A, B and C:
Where `A = [(6, -5)]; B = [(-2, 0),(4, -1)]` and `C = [(-7), (4)]`.
Given `A = [(-1, 0),(2, -4)]` and `B = [(3, -3),(-2, 0)]`; find the matrix X in the following:
X – B = A
Given `A = [(1, 4),(2, 3)] and B = |(-4-1),(-3 -2)|`
Find the matrix 2A + B
Given A = `[(-3, 6),(0, -9)]` and At is its transpose matrix. Find 2At – 3A
Given `A = [(1, 1),(-2, 0)]` and `B = [(2, -1),(1, 1)]`. Solve for matrix X:
3A – 2X = X – 2B
Given `A = [(4, 1),(2, 3)]` and `B = [(1,0),(-2, 1)]` find `A^2 - AB + 2B`
If A = `[(1, 2),(3, 4)]`, B = `[(6, 1), (1, 1)]` and C = `[(-2, -3),(0, 1)]`, find the following and state if they are equal CA + B
Find x and y, if `[(3x, 8)][(1, 4),(3, 7)] - 3[(2, -7)] = 5[(3, 2y)]`
If A = `[(5, -5),(3, -3)]` and B = `[(-5, 5),(-3, 3)]`; the value of matrix (A – B) is ______.
If `4[(5, x)] - 5[(y, -2)] = [(10, 22)]`, the values of x and y are ______.
