Multiplication Definition and 484 Threads

Hello, guys. Last week I have begin my study of linear algebra from cero. I am learining about the basics of matrices. Please, I would like to know if this is ok: 1. Let "In" be the identity matrix (n x n). 2. Let "e1" be an elementary row operation such that, applied to In, we obtain...

We are considering a system in which the input signal x(t) is multiplied by a periodic square wave s(t) in order to produce an output w(t). The input signal is band limited with |X(j\omega)| = 0 \ \ \textrm{for} \ \ |\omega| \geq \omega_M , where \omega_M is the bandwidth. We are supposed...

I have to find (a+bi)(c+di) in polar form given that b,c,d>0 and a<0. So I convert each one to polar first. ( (a+b)cis(\arctan(-b/a) + \pi) ) ( (c+d)cis(\arctan(d/c)) ) That's as far as I got. Little help please?

Let P=(p_{ij}) be a real symmetric 2x2 matrix. Show that the function on \mathbb{R}^2\times\mathbb{R}^2 (Where R^2 is a space of column vectors) defined by <v,w>=v^tPw is an inner product if and only if p_{11} and det(P) are both swtrictly positive. I just need to know what Pw means in <v,w>=v^tPw.

Mental Multiplication for 2 digit numbers and beyond 1 7 | <---- this is step one... multiply the tens place times each other. =10X10 1 7 X now we have 100. The next step will be 10X 7 either way you look at it. 17 / <---- 10 times 7 is 70... we now have a...

Hello, here is the question my book is asking: Let A, B be two m x n matricies. Assume that AX = BX for all n-tuples X. Show that A = B. ------- So I decided to try and prove the contrapositive, which is (unless I am mistaken): If A \neq B, then there is some X such that AX \neq BX Proof...

So does everybody know the Axioms of Addition and Multiplication? They are too long to type, but they are listed: A1, A2, A3, A4, A5, M1, M2, M3, M4, M5 and the distributive law, DL. anyways, I want to prove: 1. (-x)y = -(xy) and 2. (-x)(-y) = (xy) using ONLY the axioms of additon and...

Hi everybody, This may have been discussed before ( and by me) but I would like to see a proof of the following statement: " (ab)+(ac)=ab+ac" Ok let me explain a bit. When we want to set some axioms about the real numbers we say that we define two functions from RxR->R, addition(+) and...

I have a function 2-z^2-2\cos z, which has a zero at z=0. I have determined the Maclaurin series for f: \sum_{j=2}^\infty(-1)^{j-1}\frac{2z^{2j}}{(2j)!}, and now I have to determine the coefficients a_{-j},~\forall j>0, in the Laurent series for a function h, which is defined as...

for a termwise mulitiplication of two taylor series, 1.sigma a [SIZE="1"]m(x-x0)^m 2.sigma b [SIZE="1"]m (x-x0)^m then if you mutilpy 1 and 2, shouldn't you get sigma a [SIZE="1"]mb[SIZE="1"]m(x-x0)^2m? but my textbook says that it's only sigma a [SIZE="1"]mb[SIZE="1"]m(x-x0)^m from...

What is the rigorous definition of multiplication and how can it be shown to be like repeated addition ?

What was the (historical) motivation for defining the rules of matrix multiplication the way it is?

(Or if you prefer: Why are things defined this way?) I noticed that, in my book's definition, scalar multiplication (SM) on vector spaces lacks two familiar things: commutativity and inverses. The multiplicative inverse concept doesn't seem to apply to SM. Can it? I can't imagine how it could...

I am reading this table in the bookk and everyhting makes senes but I'm confused on the last part, under the Octal. For example the first line: 5x2 = 10 = 8+2 = 12, i see where the 2 came from in 12, but where did the 1 come from...also 5x6 + 1 = 31 = 24 + 7 = 37, the 7 makes sense but...

Greetings--I was wondering if someone could recommend some background reading on group theory in physics that explains group multiplication laws (I guess "tensor multiplication" is more appropriate). I.e. in SO(3), 3 x 3 = 1 + 3 + 5 So that is to say if I had two vectors, \bar{x}=(x_1...

just curious, how do you prove the basic matrix addition and scalar multiplication properties if you don't want to prove it just by giving examples?

hi all just got stuck on these questions on matrices just wondering if anyone can help me out thanks 1. For which values of k is the folowing equation satisfied? |3-k 5 | = 0 |4 4-k | its all in a matrix. I am thinking it is the determinant =0...

Hi When one is trying to multiply two matrices of different sizes e.g. a 2x3 and a 3x3. I know that one has to use the column-row-rule which states: AB_{ij} = a_{i1} b_{1j} + a_{i2} b_{2j} + \cdots + a_{i n} b_{m j} Looking at the following example: A= \left[ \begin{array}{ccc} 7...

Ok, maybe a dumb question, but anyway: if I have some matrices equation like this: AB = BC if I want to multiply both sides by some matrix Z can I stick it in the middle? AZB = BZC I know I can do these two: ABZ = BCZ ZAB = ZBC but can I do the middle too? Thanks!

I know how to solve basic problems like this, but I have no clue where to start with one of the first parts in this example. I am given the following information about C, which is a 2 X 2 matrix. C \left[ \begin{array}{cc} 1\\ 2 \end{array} \right] = \left[ \begin{array}{cc} 2\\ 1...

Hi everybody, We define multiplication as an operation with these properties : a(b+c)=ab+ac and (a+b)c=ac+bc ,a*0=0 and a*1=a with a,b,c natural numbers and of course the two properties Zurtex mentioned ab=ba and a(bc)=(ab)c-I "forgot" to mention them because I didn't use them in what is...

(a-b)X(a+b)=2(aXb), where a and b are vectors. Thank you.

Hi everybody, I just want to make something clear: does juxtaposition always show multiplication? For example 2ab(c+d)e(pi)=2*a*b*(c+d)*e*(pi) ? Generally it applies to any multiplication as long as there are no confusions,despite the number of factors?(obviously 23 is not 2*3!) ? And one...

Why does commutivity of real numbers exist for multiplication ie why a*b=b*a ? Roger

Is there an easy way to do 3 X 3 Matrix Multiplication?

For a computer program, I have to multiply: a[][] * b[] and store it in c[] how does the math for this work out on paper? What exactly am I multiplying?

I am having difficulty putting this question...i can't explain exactly what i mean Can anyone tell me in detail (history, number theory and all) about multiplication of fractions? I know that 5^2 means taking 5, 5 times and adding them. But what does 0.5^70 mean? I need indepth...

I have homework due and no help from the TA's due to a language problem. How do you multiply a scalar with a matrix? It seems so simple, but I keep getting errors, such as "matrix must be square". .m funtion code: function X=parabola(a,x,b) X=(x*a+b)^2; Command window code ...

i am curious as to how this would look. i wonder how the addition tables would look in base -5? would the multiplication look the same? here is what i know so far: addition multiplication 0 1 2 3 4...

hi guys, this is a question i got really confused on they give you a question which is 3=ln(t) * sin(t) solve for t. i don't know how to do this algebracially if it is even possible. i can do it on my calculator by sketching the graph and finding the exact value but how do you do this...

Hi, Can someone please show some example of Qualitative difference between Addition and Multiplication, when using Boolean Logic? (by Qualitative difference I mean that Quantity remains unchanged during addition or multiplication operations between n positive integers).

What does it mean to multiply two physical quantities? Ie: For electrical potential energy the equation is Ee=kq1q2/r Where k=Coulombs constant, q1 and q2 are charges in Couloumbs and r is the distance between the charges What does it mean to multiply q1 and q2?

How might one comprehend the product of complex numbers N [pi](an+ibn)=C n=1 such as by representation with vectors in the complex plane, or algebraic simplification? Specifically, I would like to know the value Re(C).

Why might two matrices commute? I.e Why would AB=BA because in general, matrices usually do not commute. What are the properties of matrices that do commute? Ben