Matrix A- 1 2 3- 1 1 5- 2 4 7 - then the value of a 31 A 31 - a 32 A 32 - a 33 A 33 is

The correct option is B 1 Given matrix is A=[ 1 amp; 2 amp; 3 1 amp; 1 amp; 5 2 amp; 4 amp; 7 ] #160; a_31=2,a ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Definition of a Determinant

Matrix A=[ ...

Question

Matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 1 & 1 & 5 2 & 4 & 7 \end{matrix} ⎤ ⎥ ⎦$ then the value of $a_{31} A_{31} + a_{32} A_{32} + a_{33} A_{33}$ is

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

13

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

- 13

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $- 1$
Given matrix is $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 1 & 1 & 5 2 & 4 & 7 \end{matrix} ⎤ ⎥ ⎦$
$a_{31} = 2, a_{32} = 4, a_{33} = 7$
$A_{31} = 10 - 3 = 7, A_{32} = 5 - 3 = 2, A_{33} = 1 - 2 = - 1$
$⟹ a_{31} A_{31} + a_{32} A_{32} + a_{33} A_{33} = (7) (2) - (4) (2) + (7) (- 1) = - 1$

Suggest Corrections

Similar questions

Q. Let

a_{n}

denote the

n^{th}

term of a geometric progression with common ratio less than

1.

a_{1} + a_{2} + a_{3} = 13

and

a_{1}^{2} + a_{2}^{2} + a_{3}^{2} = 91,

then the value of

a_{10}

Q. If a is a non-zero digit in the numbers

1 a 2 a

and

a 31

, what is the value of a when

1 a 2 a + a 31 = 2659

Q. Let

α

be a root of the equation

x^{2} + x + 1 = 0

and the matrix

A = \frac{1}{\sqrt{3}}

⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & α & α^{2} 1 & α^{2} & α^{4} \end{matrix} ⎤ ⎥ ⎦

, then the matrix

A^{31}

is equal to

Q. Let

A

be a

3 \times 3

matrix such that

a_{11} = a_{33} = 2

and all the other

a_{i j} = 1

. Let

A^{- 1} = x A^{2} + y A + z I

, then the value of

(x + y + z)

where

I

is a unit matrix of order

3

, is-

Q. Let

A

be a

3 \times 3

matrix such that

a_{11} = a_{33} = 2

and all the other

a_{i j} = 1

. Let

A^{- 1} = x A^{2} + y A - z I

, then find the value of

(x + y + z)

where

I

is a unit of matrix of order 3.

Join BYJU'S Learning Program

Matrix A=⎡⎢⎣123115247⎤⎥⎦ then the value of a31A31+a32A32+a33A33 is

The correct option is B −1Given matrix is A=⎡⎢⎣123115247⎤⎥⎦ a31=2,a32=4,a33=7A31=10−3=7,A32=5−3=2,A33=1−2=−1 ⟹a31A31+a32A32+a33A33=(7)(2)−(4)(2)+(7)(−1)=−1

Matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 1 & 1 & 5 2 & 4 & 7 \end{matrix} ⎤ ⎥ ⎦$ then the value of $a_{31} A_{31} + a_{32} A_{32} + a_{33} A_{33}$ is