Math Help - matrix

1. matrix

M is a matrix

Let m =
[
1 1 2
0 1 1
0 0 1
]

Find M^n where n is a positive integer.

2. How many powers have you tried?
It very easy to do: try n=2, 3, & 4.
You should see what the general power n is.

3. i dont understand what the question is asking. i mean if i do M^2 then isnt n a positive integer?

4. M^2=M*M
M^3=M*M^2
M^4=M*M^3
.
.
.
M^n=M*M^(n-1)

5. n=3?

6. You do know how to do matrix multiplication, don’t you?
Get m^2=m*m, then to get m^3=m*m^2.

7. Hello, Mr_Green!

I used a very primitive method . . .

M is a matrix

. - . - . . | 1 1 2 |
. . M .= .| 0 1 1 |
. - . - . . | 0 0 1 |

Find M^
n where n is a positive integer.

I cranked out the first powers and looked for a pattern.

. . . . . . . . | 1 2 5 |
. . M^
2 .= .| 0 1 2 |
. . . . . . . . | 0 0 1 |

. . . . . . . . | 1 3 9 |
. . M^
3 .= .| 0 1 3 |
. . . . . . . . | 0 0 1 |

. . . . . . . . | 1 4 14 |
. . M^
4 .= .| 0 1 -4o|
. . . . . . . . | 0 0 -1o|

. . . . . . . . | 1 5 20 |
. . M^
5 .= .| 0 1 -5o|
. . . . . . . . | 0 0 -1o|

. . . . . . . . . . . . | 1 . n . n(n+3)/2 | .**
Hence: -M^
n -= -| 0 . 1 . . . - n - - |
. . . . . . . . . . . . | 0 . 0 . . . - 1 . . |

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

**

I worked out the formula for the a
13 element
. . by examining the sequence: 2, 5, 9, 14, 20, ...
. . and constructing a quadratic function for it.