Home
Class 12
MATHS
If A =((1,0,0),(2,1,0),(3,2,1)) u(1) and...

If `A =((1,0,0),(2,1,0),(3,2,1)) u_(1) and u_(2)` are the column matrices such
that `Au_(1) = ((1),(0),(0))and Au_(2) = ((0),(1),(0))" then " u_(1) + u_(2)` is equal to

A

`((-1),(-1),(0))`

B

`((1),(-1),(-1))`

C

`((-1),(1),(0))`

D

`((-1),(1),(-1))`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `u_(1) + u_(2) = ((x),(y),(z))`
Now, `Au_(1) + Au_(2) = ((1),(1),(0))`
`rArrA(u_(1) + u_(2)) = ((1),(1),(0))`
`rArr ((1,0,0),(2,1,0),(3,2,1)) ((x),(y),(z)) = ((1),(1),(0))`
`rArr ((x),(2x+y),(3x+2y+z)) = ((1),(1),(0))`
`therefore x = 1, 2x + y =1`
and ` 3x + 2y +=0`
`rArr x=1, y=-1, z=-1` Hence, `u_(1) + u_(2) = ((1),(-1),(1))`
Promotional Banner

Similar Questions

Explore conceptually related problems

If A=[{:(0,1),(1,0):}] , then A^(2) is equal to ......

If A=[{:(1,0,0),(0,1,0),(0,0,1):}] then A^(2)+2A = ……….

Let A= [[1,0,0],[2,1,0],[3,2,1]] be a square matrix and C_(1), C_(2), C_(3) be three comumn matrices satisgying AC_(1) = [[1],[0],[0]], AC_(2) = [[2],[3],[0]] and AC_(3)= [[2],[3],[1]] of matrix B. If the matrix C= 1/3 (AcdotB). The ratio of the trace of the matrix B to the matrix C, is

If A=[{:(0,-x),(x,0):}],B=[{:(0,1),(1,0):}]andx^(2)=-1 then show that (A+B)^(2)=A^(2)+B^(2) .

The incentre of triangle with vertices (1, sqrt(3)), (0,0) and (2, 0) is

If A=[{:(2,3,-4),(5,1,0),(3,-2,5):}]andI=[{:(1,0,0),(0,1,0),(0,0,1):}] then show that AI=IA=A.

Given A=[(1,1,1),(2,4,1),(2,3,1)], B=[(2,3),(3,4)]. Find P such that BPA= [(1,0,1),(0,1,0)]

If A=[{:(1,0,1),(0,1,2),(0,0,4):}] then show that [3A]=27[A]