Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Target Exercises>Q 32

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

If $A = [\begin{array}{l} 1 & 2 \\ 5 & 4 \end{array}]$ , then a non-singular matrix $P$ such that $P^{- 1} A P = [\begin{matrix} 6 & 0 \\ 0 & - 1 \end{matrix}]$ , is

50% studentsanswered this correctly

Important Questions on Matrix

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Work Book Exercise 1.1>Q 1

A matrix

A = [a_{i j}]

is an upper triangular matrix, if

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Work Book Exercise 1.1>Q 2

If

A

is any

m \times n

matrix such that

A B

and

B A

are both defined, then

B

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Work Book Exercise 1.1>Q 3

If

A = [\begin{array}{l} 1 \\ 2 \\ 3 \end{array}]

and

B = [\begin{matrix} - 5 & 4 & 0 \\ 0 & 2 & - 1 \\ 1 & - 3 & 2 \end{matrix}]

, then

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Work Book Exercise 1.1>Q 4

If

A = [\begin{array}{r} 0 & c & - b \\ - c & 0 & a \\ b & - a & 0 \end{array}]

and

B = [\begin{array}{l} a^{2} & a b & a c \\ a b & b^{2} & b c \\ a c & b c & c^{2} \end{array}]

then

A B

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Work Book Exercise 1.1>Q 5

If

U = [\begin{array}{l} 2 & - 3 & 4 \end{array}], V = [\begin{array}{l} 3 \\ 2 \\ 1 \end{array}], X = [\begin{array}{l} 0 & 2 & 3 \end{array}]

and

Y = [\begin{array}{l} 2 \\ 2 \\ 4 \end{array}]

then the value of

U V + X Y

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Work Book Exercise 1.1>Q 6

If

A = [\begin{array}{l} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1 \end{array}]

then

A^{2}

is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Work Book Exercise 1.1>Q 7

Matrix

A

has

m

rows and

(n + 5)

columns, matrix

B

has

m

rows and

(11 - n)

columns. If both

A B

and

B A

exist, then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 1 - Matrix>Work Book Exercise 1.1>Q 8

If

A = [\begin{matrix} 1 & 0 \\ \frac{1}{2} & 1 \end{matrix}]

, then

A^{100}

is equal to