1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XIII
Mathematics
AM,GM,HM Inequality
Let A=[aij] b...
Question
Let
A
=
[
a
i
j
]
be a real matrix of order
3
×
3
, such that
a
i
1
+
a
i
2
+
a
i
3
=
1
, for
i
=
1
,
2
,
3.
Then, the sum of all the entries of the matrix
A
3
is equal to:
Open in App
Solution
Let a matrix
B
=
⎡
⎢
⎣
1
1
1
⎤
⎥
⎦
∴
A
⋅
B
=
B
Sum of all entries of
A
3
is equal to the only element of
B
T
.
A
3
.
B
∴
B
T
.
A
3
.
B
=
B
T
.
A
2
.
(
A
B
)
=
B
T
.
A
2
.
B
=
B
T
.
B
=
[
3
]
1
×
1
Suggest Corrections
0
Similar questions
Q.
Let
A
=
[
a
i
j
]
be a square matrix of order
3
such that
a
i
j
=
2
j
−
i
, for all
i
,
j
=
1
,
2
,
3
. Then, the matrix
A
2
+
A
3
+
⋯
+
A
10
is equal to:
Q.
Let
A
be a square matrix of order
3
whose all entries are
1
and let
I
3
be the identity matrix of order
3
. Then the matrix
A
−
3
I
3
is
Q.
Let
A
=
[
a
i
j
]
m
×
n
be a matrix such that
a
i
j
=
1
for all
i,j.
Then,
Q.
Let
A
be a
3
×
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.
If
A
=
[
a
i
j
]
is scalar matrix of order
n
×
n
such that
a
i
j
=
k
for all
i
, then
|
A
|
equals
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Relation between AM, GM and HM
MATHEMATICS
Watch in App
Explore more
AM,GM,HM Inequality
Standard XIII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app