If A = [1 1 1; 0 1 1; 0 0 1] and M = A + A² + A³ + .... + A²?, then the sum of all the elements of the matrix M is equal to………
If A = [1 1 1; 0 1 1; 0 0 1] and M = A + A² + A³ + .... + A²?, then the sum of all the elements of the matrix M is equal to………
-
1 Answer
-
A² = [1 2 3; 0 1 2; 0 1]
A³=A².A= [1 3 6; 0 1 3; 0 1]
A²? = [1 20 1+2+3.20; 0 1 20; 0 1] = [1 20 210; 0 1 20; 0 1]
M= [20 210 520; 0 20 210; 0 20]
M (a? )=T? =n (n+1)/2
S? = 1/2 [ n (n+1) (2n+1)/6 + n (n+1)/2 ]
⇒S? =1540
⇒M=2020
Similar Questions for you
Similarly we get A19 =
=
So, b = 2
Hence b - a = 4
Given x + 2y – 3z = a
2x + 6y – 11z = b
x – 2y + 7z = c
Here
For infinite solution
20a – 8b – 4c = 0 Þ 5a = 2b + c
Sum of all elements of [Sum of natural number upto 100 which are neither divisible by 3 nor by 5]
= 10100 – 3366 – 2100 + 630
= 5264
Kindly go through the solution
B = (I – adjA)5
N =
N =
Now
-> a100 + a2 = 2
->a =
Taking an Exam? Selecting a College?
Get authentic answers from experts, students and alumni that you won't find anywhere else
Sign Up on ShikshaOn Shiksha, get access to
- 65k Colleges
- 1.2k Exams
- 687k Reviews
- 1800k Answers