My Math Forum Matrix question (confusing)

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 December 21st, 2010, 11:26 PM #1 Senior Member   Joined: Dec 2010 Posts: 233 Thanks: 0 Matrix question (confusing) Given that A=( ) a11=2, a12=2, a21=3, a22=-1, (it is a matrix, sorry I can't type matrix in word) find A^2 and A^3. If f(x)= x^3-3x^2-2x+4, find f(A). If g(x)=x^2-x-8, find g(A). I have solved many kinds of problem in matrix, but this confusing me a lot. I dunno how to do. I only can find A^2 and A^3. Please help me step by step.
 December 22nd, 2010, 05:25 AM #2 Senior Member   Joined: Dec 2010 Posts: 233 Thanks: 0 Re: Matrix question (confusing) help me !!!
 December 22nd, 2010, 07:40 AM #3 Global Moderator   Joined: Dec 2006 Posts: 19,882 Thanks: 1835 $\begin{pmatrix} 2 & 2 \\ 3 & -1 \end{pmatrix}\begin{pmatrix} 2 & 2 \\ 3 & -1 \end{pmatrix}=\begin{pmatrix} 10 & 2 \\ 3 & 7 \end{pmatrix}$ $\begin{pmatrix} 2 & 2 \\ 3 & -1 \end{pmatrix}\begin{pmatrix} 10 & 2 \\ 3 & 7 \end{pmatrix}=\begin{pmatrix} 26 & 18 \\ 27 & -1 \end{pmatrix}$ To add matrices (of the same size), add corresponding elements. To multiply a matrix by a constant, multiply each element of the matrix by the constant. I suggest interpreting "+ 4" and "- 8" as "+ 4I" and "- 8I", where I is the identity matrix (having 1 as each element of the main diagonal, and zero for all the other elements). Hence g(A) = A² - A - 8I = $\begin{pmatrix} 10 & 2 \\ 3 & 7 \end{pmatrix}-\begin{pmatrix} 2 & 2 \\ 3 & -1 \end{pmatrix}-\begin{pmatrix} 8 & 0 \\ 0 & 8 \end{pmatrix}=\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}$ Can you complete the answer by finding f(A) now?
 December 23rd, 2010, 06:58 AM #4 Senior Member   Joined: Dec 2010 Posts: 233 Thanks: 0 Re: Matrix question (confusing) I don't really understand. Anyone else can help?
 December 23rd, 2010, 09:01 AM #5 Global Moderator   Joined: Dec 2006 Posts: 19,882 Thanks: 1835 Can you be more specific? For example, do you know how matrix multiplication is done?
 December 30th, 2010, 09:28 PM #6 Newbie   Joined: Dec 2010 From: india Posts: 1 Thanks: 0 Re: Matrix question (confusing) Hi, Dear hoyy1kolko, I understand your problem. I suggest this site for your problems. This is an easy calculation site for all math problems.

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