Question

find the product [-1,7 7,7][-9,-4 -4,3]

Answer 1

2-by-2 matrix or 4 element vectors?

Answer 2

2 by 2 matrix

Answer 3

sorry 4 element vectors.

Answer 4

Let \[A = \left[\begin{matrix}a & b \\ c & d\end{matrix}\right] ~~\text{and}~~ B = \left[\begin{matrix}1 & 2 \\ 3 & 4\end{matrix}\right]\]I find it easier to write the matrices with the following orientation. This way it is easier to multiply the rows and columns. \[\begin{matrix}& \left[\begin{matrix}1 & 2 \\ 3 & 4\end{matrix}\right] \\ \left[\begin{matrix}a & b \\ c & d\end{matrix}\right] & \left[ \begin{matrix} w & x \\ y & z \end{matrix} \right] \end{matrix}\]Now let's work through it.
\[\begin{matrix}w = a*1 + b*3 & x =a*2 + b*4 \\ y = c*1+d*3 & z = c*2 + d*4 \end{matrix}\]

Answer 5

Okay now how do I add and multiply these?
I am not very good at math and have a hard time with it

Answer 6

Is that the correct form? The above solution is for a matrix. I can do it for a vector if that is what is required. A vector looks like this \[V = \left(\begin{matrix}a \\ b\\c\\d\end{matrix}\right)\]

Answer 7

no it's a matrix it has 4 numbers within two brackets

Answer 8

Got it. What I gave you above is for multiplication of two matrices. I'll walk you through multiplying a matrix by a scaler and adding matrices.

Again, let \[A =\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]~~ \text{and}~~ B = \left[\begin{matrix} 1 & 2\\3& 4 \end{matrix} \right]\]If we multiply A by some number x, we get \[xA = \left[\begin{matrix}x*a & x*b \\ x*c & x*d\end{matrix}\right]\]Now lets add A and B\[A + B = \left[\begin{matrix}a+1 & b+2 \\ c+3 & d+4\end{matrix}\right]\]Here 1,2,3, and 4 refer to the elements of B, not numbers.

Answer 9

okay

Answer 10

This make sense?

Answer 11

somewhat

Answer 12

Okay. How about I walk you through it?

We are multiplying a 2-by-2 with a 2-by-2. We will end with a 2-by-2 matrix. When we multiply two matrices, the number of columns of the first must equal the number of rows of the second. We end up with a matrix that has the same number of rows as the first by the same number of columns of the second. A 3x4 times a 4x5 yields a 3x5 matrix. Make note of this.

Now, let's write the matrix out in this handy form. \[\begin{matrix} & \left[\begin{matrix}-9 & -4 \\ -4 & 3\end{matrix}\right]\\ \left[\begin{matrix}-1 & 7 \\ 7 & 7\end{matrix}\right] & \left[\begin{matrix}w & x \\ y & z\end{matrix}\right]\end{matrix}\]where the w,x,y,z matrix is the answer. Now we need to multiply the elements of the first matrix's rows with the elements of the second matrix's columns. This becomes\[\left[\begin{matrix}(-1)(-9) + (7)(-4) & (-1)(-4) + (7)(3) \\ (7)(-9) + (7)(-4) & (7)(-4) + (7)(3)\end{matrix}\right]=\left[\begin{matrix}19 & 25 \\ -91 & -7\end{matrix}\right]\]