NDA 2017 Paper 2 | Matrices Question 14 | Mathematics

The matrix A has x rows and x + 5 columns. The matrix B has y rows and 11 $$-$$ y columns. Both AB and BA exist. What are the values of x and y respectively?

8 and 3

3 and 4

3 and 8

8 and 8

NDA 2017 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

If A is a square matrix, then the value of adj $${A^T}$$ $$-$$ (adj $${A)^T}$$ is equal to

2 | A| I, where I is the identity matrix

null matrix whose order is same as that of A

unit matrix whose order is same as that of A

NDA 2017 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

The adjoint of the matrix $$A = \left[ {\matrix{ 1 & 0 & 2 \cr 2 & 1 & 0 \cr 0 & 3 & 1 \cr } } \right]$$ is

$$\left[ {\matrix{ { - 1} & 6 & 2 \cr { - 2} & 1 & { - 4} \cr 6 & 3 & 1 \cr } } \right]$$

$$\left[ {\matrix{ 1 & 6 & { - 2} \cr { - 2} & 1 & 4 \cr 6 & { - 3} & 1 \cr } } \right]$$

$$\left[ {\matrix{ 6 & 1 & 2 \cr 4 & { - 1} & 2 \cr 6 & 3 & { - 1} \cr } } \right]$$

$$\left[ {\matrix{ { - 6} & 2 & 1 \cr 4 & { - 2} & 1 \cr 3 & 1 & { - 6} \cr } } \right]$$

NDA 2017 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

If a, b, c are non-zero real numbers, then the inverse of the matrix $$A = \left[ {\matrix{ a & 0 & 0 \cr 0 & b & 0 \cr 0 & 0 & c \cr } } \right]$$ is equal to

$$\left[ {\matrix{ {{a^{ - 1}}} & 0 & 0 \cr 0 & {{b^{ - 1}}} & 0 \cr 0 & 0 & {{c^{ - 1}}} \cr } } \right]$$

$${1 \over {abc}}\left[ {\matrix{ {{a^{ - 1}}} & 0 & 0 \cr 0 & {{b^{ - 1}}} & 0 \cr 0 & 0 & {{c^{ - 1}}} \cr } } \right]$$

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

$${1 \over {abc}}\left[ {\matrix{ a & 0 & 0 \cr 0 & b & 0 \cr 0 & 0 & c \cr } } \right]$$

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