- #1
niteshadw
- 20
- 0
(1)
Let
A =
2 0
4 1
B =
2 0 −4
3 −2 6
C =
5 0 0
0 −1 0
0 0 0
and let f(t) = t^2 - 5t + 2. Compute the following if possible.
(a) A^3
(b) C^2003
(e) f(A)
(g) We define the matrix exponential by the Taylor series:
e^C = I + C + 1/2! * C^2 + 1/3! * C^3 + · · · + 1/n! * Cn + · · · .
Calculate e^C
(2)
An n × n matrix S (with real entries) is called a square root of the n × n matrix A (with real entries), if S2 = A.
Find the square roots of the matrix
A=
1 3
0 1
========================
I don't have an idea on how to do the problems just posted, I can do the rest and those that I did not post, but I never learned #2 and I don't know how to take powers of matrix nor recall series. Would anyone be kind enough to explain how to do these problems. It would be very much appreciated. Thank you.
Let
A =
2 0
4 1
B =
2 0 −4
3 −2 6
C =
5 0 0
0 −1 0
0 0 0
and let f(t) = t^2 - 5t + 2. Compute the following if possible.
(a) A^3
(b) C^2003
(e) f(A)
(g) We define the matrix exponential by the Taylor series:
e^C = I + C + 1/2! * C^2 + 1/3! * C^3 + · · · + 1/n! * Cn + · · · .
Calculate e^C
(2)
An n × n matrix S (with real entries) is called a square root of the n × n matrix A (with real entries), if S2 = A.
Find the square roots of the matrix
A=
1 3
0 1
========================
I don't have an idea on how to do the problems just posted, I can do the rest and those that I did not post, but I never learned #2 and I don't know how to take powers of matrix nor recall series. Would anyone be kind enough to explain how to do these problems. It would be very much appreciated. Thank you.