First of all, if we have any two matrices of sizes mxn and pxq where m, n, p and q are natural numbers, then we must have n=p to be able to multiply the matrices. The result is an mxq matrix. For example, a 3x1 matrix has m=3 and n=1. We can multiply it with any matrix of size 1xq. For example a 2x3 matrix can be multiplied with a 3x1 matrix which has 3 rows and 1 column and the result is a 2x1 matrix. (2x3) multiplies by (3x1) gives a (2x1) matrix. The easy way to remember this is write the dimension of Matrix A and then Matrix B. The two inner numbers must be the same and the two outer numbers are the dimensions of the matrix you have after multiplication. For example Let Matrix A have dimensions (axb) multiply it by matrix B which has dimensions (bxc) = the result is matrix of dimensions ac. Using the trick we would remind ourselves by writing (a,b)x(b,c)=(a,c). This is technically wrong because the numbers are dimensions, but it is just a method to help students remember how to do it. So, a 3x3 matrix can be multiplied by a 3x 1 but not by a 1,3 matrix. How do you do it? Just multiply each entry in the first row of A by each entry in the first column of B and add the products. Do the same for the next row etc. Many (or should I honestly say MOST) people use their fingers and go along row one and then down column one. The add the products of the entries as they do that. Then they do the same for row two and column two etc. It really does help!
3 x 1 = 3
(3x1) + (5/10)
How to solve a system of linear equations 1. arrange all of them in standard form. standard form has all variables in the same order beginning with the lowest power variables on the left and ending with the highest power variables on the right. This will be equal to the number without a variable on the right side of the equation. If there are missing variables or numbers, put in a zero in it's place. 2. Using a TI-83: Press these keys: 2nd, matrix, >>, enter. Type how many rows your matrix has (if you have 3 equations, you need 3 rows). Press enter. Type how many columns your matrix has (if you have x^3, x^2, and x on one side of the equal sign, you need 3 columns). Press enter. Begin entering your data, ignoring the number on the right side of the equals sign. When finished, press 2nd, quit. 3. Press 2nd, matrix, >>, down, enter. Using the example from above with the 3 equations, you now need a 3x1 matrix. When finished entering data, press 2nd, quit. 4. Press 2nd, matrix. Hilight the 3x3 matrix you created, press enter. Press the x^-1 key. Press 2nd, matrix. Hilight the 3x1 matrix, press enter, enter. And wall-a, there you have your answers!! If you were to solve it by hand, just solve two of the equations for a different variable and plug the solved equations into the unsolved equation and solve. This way can get hairy, but it also works fine.
1x3 and 3x1 FActors are 1,3
(2x4)+(3x1)+(1x7) = 18
No, that's associative.
The number equivalent to one 10 and three 1 is the same, As 1x10=10 And 3x1=3 :)
3x1=3, in this case 3x11=33.
1x3 and 3x1 and -1x-3 and -3x-1
The Multiplicative Property of 1.
3 3x1=3 3x3=9
you read it like this 3x1=3 genius
If you are asking for the answer to 5x3 over 3x1, it is 5.
Multiply the number 3 times its place value. 1/10, 1/100, 1/1000, 1/10000 3x1/10=3/10
multiply the one and the three 3x1=3....then add the zeros. 300000000000000 is the answer. your either really young, or bored.
he zero isn'treally necessary. that would be 2x1/10+5x1/100+3x1/1000 Thanks.