1
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-1

$$A=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right]$$, if $$U_{1}, U_{2}$$ and $$U_{3}$$ are columns matrices satisfying. $$\mathrm{AU}_{1}=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], \quad \mathrm{AU}_{2}=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], \quad \mathrm{AU}_{3}=\left[\begin{array}{l}2 \\ 3 \\ 1\end{array}\right]$$ and $$\mathrm{U}$$ is $$3 \times 3$$ matrix whose columns are $$\mathrm{U}_{1}, \mathrm{U}_{2}, \mathrm{U}_{3}$$ then answer the following questions

The value of $$|U|$$ is :
A
3
B
$$-3$$
C
$$3 / 2$$
D
2
2
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-1

Comprehension IV

$\mathrm{A}=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right]$, if $\mathrm{U}_1, \mathrm{U}_2$ and $\mathrm{U}_3$ are columns matrices satisfying. $\mathrm{AU}_1=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], \mathrm{AU}_2=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], \mathrm{AU}_3=\left[\begin{array}{l}2 \\ 3 \\ 1\end{array}\right]$ and U is $3 \times 3$ matrix whose columns are $\mathrm{U}_1, \mathrm{U}_2, \mathrm{U}_3$ then answer the following questions

The sum of the elements of $\mathrm{U}^{-1}$ is:

A

-1

B

0

C

1

D

3

3
IIT-JEE 2006
MCQ (Single Correct Answer)
+3
-1

$\mathrm{A}=\left[\begin{array}{lll}1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1\end{array}\right]$, if $\mathrm{U}_1, \mathrm{U}_2$ and $\mathrm{U}_3$ are columns matrices satisfying. $\mathrm{AU}_1=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right], \mathrm{AU}_2=\left[\begin{array}{l}2 \\ 3 \\ 0\end{array}\right], \mathrm{AU}_3=\left[\begin{array}{l}2 \\ 3 \\ 1\end{array}\right]$ and U is $3 \times 3$ matrix whose columns are $\mathrm{U}_1, \mathrm{U}_2, \mathrm{U}_3$ then answer the following questions

The value of $\left[\begin{array}{lll}3 & 2 & 0\end{array}\right] U\left[\begin{array}{l}3 \\ 2 \\ 0\end{array}\right]$ is :

A

5

B

$5 / 2$

C

4

D

$3 / 2$

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