AIEEE 2012 | Matrices and Determinants Question 222 | Mathematics

AIEEE 2012

MCQ (Single Correct Answer)

-1

Let $$P$$ and $$Q$$ be $$3 \times 3$$ matrices $$P \ne Q.$$ If $${P^3} = {Q^3}$$ and
$${P^2}Q = {Q^2}P$$ then determinant of $$\left( {{P^2} + {Q^2}} \right)$$ is equal to :

$$-2$$

$$1$$

$$0$$

$$-1$$

AIEEE 2011

MCQ (Single Correct Answer)

-1

Let $$A$$ and $$B$$ be two symmetric matrices of order $$3$$.
Statement - 1: $$A(BA)$$ and $$(AB)$$$$A$$ are symmetric matrices.
Statement - 2: $$AB$$ is symmetric matrix if matrix multiplication of $$A$$ with $$B$$ is commutative.

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 2011

MCQ (Single Correct Answer)

-1

The number of values of $$k$$ for which the linear equations
$$4x + ky + 2z = 0,kx + 4y + z = 0$$ and $$2x+2y+z=0$$ possess a non-zero solution is

$$2$$

$$1$$

zero

$$3$$

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.

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