AIEEE 2010 | Matrices and Determinants Question 225 | Mathematics

AIEEE 2010

MCQ (Single Correct Answer)

-1

Let $$A$$ be a $$\,2 \times 2$$ matrix with non-zero entries and let $${A^2} = I,$$
where $$I$$ is $$2 \times 2$$ identity matrix. Define
$$Tr$$$$(A)=$$ sum of diagonal elements of $$A$$ and $$\left| A \right| = $$ determinant of matrix $$A$$.
Statement- 1: $$Tr$$$$(A)=0$$.
Statement- 2: $$\left| A \right| = 1$$ .

statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1.

statement - 1 is true, statement - 2 is false.

statement - 1 is false, statement -2 is true

statement -1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1.

AIEEE 2010

MCQ (Single Correct Answer)

-1

Consider the system of linear equations; $$$\matrix{ {{x_1} + 2{x_2} + {x_3} = 3} \cr {2{x_1} + 3{x_2} + {x_3} = 3} \cr {3{x_1} + 5{x_2} + 2{x_3} = 1} \cr } $$$
The system has

exactly $$3$$ solutions

a unique solution

no solution

infinitenumber of solutions

AIEEE 2010

MCQ (Single Correct Answer)

-1

The number of $$3 \times 3$$ non-singular matrices, with four entries as $$1$$ and all other entries as $$0$$, is

$$5$$

$$6$$

at least $$7$$

less than $$4$$

AIEEE 2009

MCQ (Single Correct Answer)

-1

Let $$A$$ be a $$\,2 \times 2$$ matrix
Statement - 1 : $$adj\left( {adj\,A} \right) = A$$
Statement - 2 :$$\left| {adj\,A} \right| = \left| A \right|$$

statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1.

statement - 1 is true, statement - 2 is false.

statement - 1 is false, statement -2 is true

statement -1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1.

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