NDA 2015 Paper 2 | Matrices Question 1 | Mathematics

The matrix $$A = \left[ {\matrix{ 1 & 3 & 2 \cr 1 & {x - 1} & 1 \cr 2 & 7 & {x - 3} \cr } } \right]$$ will have inverse for every real number x except for

$$x = {{11\, \pm \sqrt 5 } \over 2}$$

$$x = {{9\, \pm \sqrt 5 } \over 2}$$

$$x = {{11\, \pm \sqrt 3 } \over 2}$$

$$x = {{9\, \pm \sqrt 3 } \over 2}$$

NDA 2015 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

If $$A = \left[ {\matrix{ 1 & 0 & { - 2} \cr 2 & { - 3} & 4 \cr } } \right]$$, then the matrix X for which 2X + 3A = 0 holds true is

$$\left[ {\matrix{ { - {3 \over 2}} & 0 & { - 3} \cr { - 3} & { - {9 \over 2}} & { - 6} \cr } } \right]$$

$$\left[ {\matrix{ {{3 \over 2}} & 0 & { - 3} \cr 3 & { - {9 \over 2}} & { - 6} \cr } } \right]$$

$$\left[ {\matrix{ {{3 \over 2}} & 0 & 3 \cr 3 & {{9 \over 2}} & 6 \cr } } \right]$$

$$\left[ {\matrix{ { - {3 \over 2}} & 0 & 3 \cr { - 3} & {{9 \over 2}} & { - 6} \cr } } \right]$$

NDA 2015 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

If $$A = \left[ {\matrix{ 1 & 1 & { - 1} \cr 2 & { - 3} & 4 \cr 3 & { - 2} & 3 \cr } } \right]$$ and $$B = \left[ {\matrix{ { - 1} & { - 2} & { - 1} \cr 6 & {12} & 6 \cr 5 & {10} & 5 \cr } } \right]$$, then which of the following is/are correct?

1. A and B commute.

2. AB is a null matrix.

Select the correct answer using the codes given below.

Only 1

Only 2

Both 1 and 2

Neither 1 nor 2

NDA 2015 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

Which one of the following matrices is an elementary matrix?

$$\left[ {\matrix{ 1 & 0 & 0 \cr 0 & 0 & 0 \cr 0 & 0 & 1 \cr } } \right]$$

$$\left[ {\matrix{ 1 & 5 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right]$$

$$\left[ {\matrix{ 0 & 2 & 0 \cr 1 & 0 & 0 \cr 0 & 0 & 1 \cr } } \right]$$