Let $A=\left(\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right)$. If $u_{1}$ and $u_{2}$ are column matrices such that $A u_{1}=\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$ and $A u_{2}=\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right)$, then $u_{1}+u_{2}$ is equal to

(D) $\left(\begin{array}{c}1 \\ -1 \\ -1\end{array}\right)$

(A) $\left(\begin{array}{c}-1 \\ 1 \\ 0\end{array}\right)$

(B) $\left(\begin{array}{c}-1 \\ 1 \\ -1\end{array}\right)$

(C) $\left(\begin{array}{c}-1 \\ -1 \\ 0\end{array}\right)$

JEE Main · 2012 · 29 Apr 2012 · Offline · Matrices

Let

A = 123012001

. If

u_{1}

and

u_{2}

are column matrices such that

A u_{1} = 100

and

A u_{2} = 010

, then

u_{1} + u_{2}

is equal to

Answer: (D)

Solving

A u_{1} = 100

row by row with the lower-triangular matrix gives

a = 1

, then

2 a + b = 0

b = - 2

, then

3 a + 2 b + c = 0

c = 1

; thus

u_{1} = (1, - 2, 1)^{T}

. In the same way

A u_{2} = 010

gives

d = 0

e = 1

f = - 2

, so

u_{2} = (0, 1, - 2)^{T}

. Adding the two columns gives

u_{1} + u_{2} = (1, - 1, - 1)^{T}

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option