I am having trouble solving this 3x3 matrix?

Question

3 0 3 ..... 1 0 0
1 2 1 ..... 4 1 1
2 -1 0 ..... -5 0 2

those are the matrix's that need multiplying.

i think you either have to multiply row 1 on matrix A, by row 1 on Matrix B.

Or you multiply row 1 on matrix A, by collom 1 on matrix B

Answer 1

-12 0 6

4 2 4

-2 -1 -1



a.b.c.......j.k.l

d.e.f.. X..m.n.o =

g.h.i........p.q.r



aj+bm+cp...ak+bn+cq...al+bo+cr

dj+em+fp ....dk+en+fq...dl+eo+fr

gj+hm+ip.... gk+hn+iq...gl+ho+ir



Let the .... be space.

Answer 2

[ 3 0 3 ] [ 1 0 0 ]

[ 1 2 1 ] * [ 4 1 1 ] <-- best attempt at matrices.

[2 -1 0 ] [ -5 0 2 ]



To do this, you need to:

(multiply the first number in row 1 of the first matrix by the first number in column 1 of the second matrix) + (multiply the second number in row 1 of the first matrix by the second number in column 1 of the second matrix) + (multiply the third number in row 1 of the first matrix by the third number in column 1 of the second matrix).



Do this for every row of matrix one and every column of matrix 2. This is why for multiplying matrices, the columns of the first matrix must equal the rows of the second matrix and the answer will have the dimensions: (rows of 1st matrix) X (columns of 2nd matrix).



To do this on a graphing calculator (TI-83+ for me) do this:

- 2nd Matrix (button text says x^-1 ... left side of the calculator)

- scroll across the top to "Edit"

- choose to edit [ A ] and enter the dimesions of the first matrix at the top.

- enter the numbers of the 1st matrix into [ A ] below. Scroll to the first position and press '3' then press 'enter'. It will scroll to the right (where you would do '0' then 'enter' then '3' and 'enter') then down, like reading a book.

- when done with [A] do 2nd -> Quit

- go to the 'matrix' dialogue again (2nd -> Matrix)

- scroll to edit and enter the dimensions and numbers of the 2nd matrix for [B]

- 2nd -> quit

- Return to 2nd->Matrix but this time don't scroll over. Now, select "1. [A]". This will put the first matrix into the field (but all you should see it say is [A].)

- Press multiply (which is the operation you want).

- Now select [B] the same way you selected [A]

- Press enter.



Hope it helps.

Answer 3

Your second thought was correct. You must multiply row 1 of the first matrix by column 1 of the second matrix. This is done by:



3x1 + 0x4 + 3x-5 = -12



So, -12 is the first entry of the first row of your answer. Your answer will be a three by three matrix. To find the answer for the second entry of the first row, you must multiply the 1st row of the first matrix by the second column of the second matrix in the same manner as above. You final answer should be:



-12 0 6

4 2 4

-2 -1 -1



(I did this in my head, so you should double check my arithmetic).



Hope this helps.

Answer 4

It's row one on A by column 1 on B. This will give you the entry of row 1, col 1 in the new matrix.

3(1) + 0(4) + 3(-5) = 3+0-15 = -12

For the entry, row1, col2, multiply row one of A and col two of B

3(0) + 0(1) + 3(0) = 0+0+0 = 0

Do you have the hang of it now?

Answer 5

3 0 3........1 0 0 = 3 0 0

1 2 1 ........4 1 1 = 4 2 1

2 1 0 ........-5 0 2 = -10 0 0



i hope this helps

multiply each number by the number in the same place of the other matrix

Answer 6

I assume that you want AB (matrix multiplication is NOT communitative)



The dot product of row i of A with col j of B gives element Cij , the element in the i row and j col of the result.



I'll get C22 = (1,2,1) dot (0,1,0) = 1*0+2*1+1*0 = 2