Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 56

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IMPORTANT

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If $x, y$ and $z$ are all distinct and $|\begin{array}{l} x & x^{2} & 1 + x^{3} \\ y & y^{2} & 1 + y^{3} \\ z & z^{2} & 1 + z^{3} \end{array}| = 0$ , then the value of $x y z$ is

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Important Questions on Matrices and Determinants

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 57

If

x_{1}, x_{2}, x_{3}, \dots, x_{13}

are in

AP

, then the value of

|\begin{array}{l} e^{x_{1}} & e^{x_{4}} & e^{x_{7}} \\ e^{x_{4}} & e^{x_{7}} & e^{x_{10}} \\ e^{x_{7}} & e^{x_{10}} & e^{x_{13}} \end{array}|

is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 58

Let

| A | = {|a_{i j}|}_{3 \times 3} \neq 0

. Each element

a_{i j}

is multiplied by

k^{i - j}

. Let

| B |

be the resulting determinant, where

k_{1} | A | + k_{2} | B | = 0

, then

k_{1} + k_{2} = ?

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 59

If

a, b

and

c

are in arithmetic progression, then the value of the determinant

|\begin{matrix} x + 2 & x + 3 & x + 2 a \\ x + 3 & x + 4 & x + 2 b \\ x + 4 & x + 5 & x + 2 c \end{matrix}|

is -

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 60

If

x, y

and

z

are greater than

1

, then the value of

|\begin{matrix} 1 & \log_{x} y & \log_{x} z \\ \log_{y} x & 1 & \log_{y} z \\ \log_{z} x & \log_{z} y & 1 \end{matrix}|

is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 61

If

k \in R

and

det A = |\begin{array}{l} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{array}| = K

then

\det B = |\begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} + 2 a_{1} & b_{2} + 2 b_{1} & c_{2} + 2 c_{1} \\ a_{3} & b_{3} & c_{3} \end{matrix}|

is equal to

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 62

The following system of linear equations

2 x + 3 y + 2 z = 9

3 x + 2 y + 2 z = 9

x - y + 4 z = 8

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 63

The system of equations $a x - y - z = a - 1$ , $x - a y - z = a - 1$ , $x - y - a z = a - 1$ has no solution if $' a'$ is

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Mathematics Crash Course JEE Main>Chapter 19 - Matrices and Determinants>Level 1>Q 64

The system of linear equations

k x + y + z = 1

,

x + k y + z = 1

and

x + y + k z = 1

has a unique solution under which one of the following conditions?