scalar multiplication
Multiply each element of the matrix by the scalar.
Add, subtract, multiply and divide.
Because multiplication is a binary operation that is defined so that it is valid for all numbers.
Yes, the result is a 3x3 matrix
scalar multiplication
You can definitely multiply 2x2 matrices with each other. In fact you can multiply a AxB matrix with a BxC matrix, where A, B, and C are natural numbers. That is, the number of columns of the first matrix must equal the number of rows of the second matrix--we call this "inner dimensions must match."
Multiply each element of the matrix by the scalar.
Add, subtract, multiply and divide.
Because multiplication is a binary operation that is defined so that it is valid for all numbers.
commutative
Yes, the result is a 3x3 matrix
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!
Multiplication is a binary operation. That means you need to have two (or more) numbers that you multiply together to get an answer. There is only one number in your question.
No.When you multiply two negative numbers together, you do not get a negative number as the answer.
Multiply it by the identity matrix.
Factors,are the number that can be multiply and multiplies are the operation to solve a problem and to factorize numbers...