CameraIcon

SearchIcon

MyQuestionIcon

442

You visited us 442 times! Enjoying our articles? Unlock Full Access!

Scalar Matrix

Let A be a 3×...

Question

Let $A$ be a $3 \times 3$ matrix and $A^{T}$ be transpose matrix of $A .$ If $A = 3 A^{T} - 4 I,$ where $I$ is identity matrix of order $3,$ then $det (A)$ is equal to

A

2

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

B

5

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

C

8

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

D

10

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

Open in App

Solution

The correct option is C $8$
$A = 3 A^{T} - 4 I$
Since $A^{T} = 3 A - 4 I$
$∴ A = 3 (3 A - 4 I) - 4 I$
$\Rightarrow A = 9 A - 16 I$
$\Rightarrow A = 2 I$
$\Rightarrow | A | = | 2 I | = 2^{3} \cdot 1 = 8$

Suggest Corrections

thumbs-up

0

Similar questions

A

is a square matrix of order

3

A^{'}

denotes transpose of matrix

A, i f A = A^{'}

d e t A = 1

d e t (A - I)

must be equal to

A

3 \times 2

matrix with real entries. Let

H = A (A^{T} A)^{- 1} A^{T}

A^{T}

is the transpose of

A

I

be the identity matrix of order

3 \times 3

A

be a square matrix of order

3

whose all entries are

1

I_{3}

be the identity matrix of order

3

. Then the matrix

A - 3 I_{3}

P = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 4 & 1 & 0 16 & 4 & 1 \end{matrix} ⎤ ⎥ ⎦

I

be the identity matrix of order

3

Q = [q_{i j}]

is a matrix, such that

p^{50} - Q = I

\frac{q_{31} + q_{32}}{q_{21}}

P = ⎡ ⎢ ⎣ \begin{matrix} 1416 \end{matrix} \begin{matrix} 014 \end{matrix} \begin{matrix} 001 \end{matrix} ⎤ ⎥ ⎦

I

be the identity matrix of order

3

Q = [q_{i j}]

is a matrix such that

P^{50} - Q = I

\frac{q_{31} + q_{32}}{q_{21}}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Types of Matrices

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon