MyQuestionIcon

1

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

Skew Symmetric Matrix

If A= [ aii...

Question

If $A = [a_{i i}]$ is a skew-symmetric matrix of order n, then $\sum a_{i i} =$

A

0

for some

i

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

B

0

for all

i = 1, 2, . . ., n

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

C

1

for some

i

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

D

1

for all

i = 1, 2, . . ., n .

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

Open in App

Solution

The correct option is B $0$ for all $i = 1, 2, . . ., n$
By definition of skew-symmetric matrix.
Diagonal elements of a skew-symmetric matrix are all 0.

Suggest Corrections

thumbs-up

0

Similar questions

Q. If A = [a_ij] is a scalar matrix of order n × n such that a_ii = k, for all i, then trace of A is equal to
(a) nk
(b) n + k
(c)

\frac{n}{k}

(d) none of these

Q. Unit matrix is a diagonal matrix in which all the diagonal elements are unity. Unit matrix of order

^{'} n^{'}

I_{n} (o r I)

A = [a_{i j}]_{n}

is a unit matrix when

a_{i j} = 0

i \neq j a n d a_{i j} = 1

i ==

.

z_{1}

is a root of the equation

a_{0} z^{n} + a_{1} z^{n - 1} + . . . . . + a_{n - 1} z + a_{n} = 4

| a_{i} | < 2

i = 0, 1, 2, . . . ., n

3 \times 3

M

N

, which of
the following statement(s) is (are)

N O T

I

N^{T} M N

is symmetric or skew-symmetric, according as

M

is symmetric or skew-symmetric

I I

M N - N M

is skew-symmetric for all symmetric matrices

M

N

I I I

M N

is symmetric for all symmetric matrices

M

N

I V

(a d j M) (a d j N) = a d j (M N)

for all invertible matrices

M

N

a > b > 0

I (n) = a^{1 / n} - b^{1 / n},

J (n) = (a - b)^{1 / n}

n \geq 2

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Symmetric Matrix

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Skew Symmetric Matrix

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon