Multiplying Matrices???

Question

{0 -1} {3 5 -2}
{-1 0} X {4 6 -3}

What is the pattern for multiplying 2x2 and 2x3 matrices??

Answer 1

pair up 1st row of 1st matrix with 1st column of 2nd, multiply pairs, add: 0(3) + (-1)(4) = -4. this is 1st row, 1st column element of 2x3 answer.

pair up 1st row of 1st matrix with 2nd column of 2nd, multiply pairs, add: 0(5) + (-1)(6) = -6. this is 1st row, 2nd column element of answer.

see what's happening? 1st row of answer will be 2nd row of 2nd matrix but with opposite signs, and 2nd row of answer will be 1st row of 2nd matrix but with opposite signs. it's not always that way. here it's the effect of that first matrix, a variation of the identity matrix.

Answer 2

The pattern for multiplying matrices is row of the first one by the column of the second. So the ii entry of the result will be 0 times 3 plus -1 times 4 = -4.

Answer 3

Understand multiplication of matrices. Click on the Link to Watch the VIDEO explanation:
http://bit.ly/13uvfJn

Multiplications Of Matrices - Numerical
Let us solve the numerical on multiplication of matrices.
Problem:
If P = matrix 5 2 2 1 and Q = 1 0 0 1 find PQ.
Let us see if the two matrices P and Q are multipliable the condition for multiplying two matrices is. two matrices A and B can be multiplied if the number of columns of A = number of rows of B. The resulted matrix will be of the order number of rows A = number of columns of B . i.e. if A be a matrix of order m by n and b be a matrix of order n by q. then A and B can be multiplied and there product will be a matrix of order m by q.
Here, in this example matrix B is of the order 2 by 2 and the matrix Q is of the order 2 by 2 so they can multiplied since the no. of columns in matrix B is equal the no. of rows in matrix Q i.e. 2.
Therefore the order of matrix PQ will be 2 by 2. Now let us understand how to multiply the matrix P and matrix Q. Matrices P and Q can be multiplied by using the row column multiplication technique as illustrated below:
Multiply the first row first column element of matrix P with a first row first column element of matrix Q then multiply the first row second column element of matrix P with the second row first column element of matrix Q in the matrix PQ you have now got 5*1 + 2*0 this will be first row first column element of matrix PQ continue the process to get the remaining element of the matrix PQ. Thus, we get PQ = matrix is 5 2 2 1 which is of the order 2 by 2. Now that matrix PQ = matrix P.
Hence matrix Q is an identity matrix we called a definition of the identity matrix a square matrix in which every diagonal element is 1 and every non diagonal element is 0 is called an identity or unit matrix and the property of an identity matrix is when a matrix is multiplied by an identity matrix we get the same matrix i.e. A*I = A = I*A.
Click on the exercise button at the bottom right of your screen and solve the problem.

Answer 4

(0*3 -1*4 0*5 - 1*6 0*2 -1*-3)
(-1*3 + 0*4 -1*5 + 0*6 -1*-2 + 0*-3)

(-4 -6 3)
(-3 -5 2)

Answer 5

You'll get a 2x3 matrix.
|-4 -6 3|
|-3 -5 2|

The pattern is that you switch the two rows and change the sign of each element.

Answer 6

Need to rearrange the matrices, so they make sense. The pattern in matrix multiplication is to realize that for multiplication to be defined the matrices must be of the form,

a x n and nx b - the number of columns in the first matrix must be equal to the number of rows of the second matrix.

suggest you re-write the matrices the follwing way:

Matrix A = 2 x 2
First row = a11, a12
Second row = a21 a22

a11 = first row, first column entry

and so forth. Good luck!

Answer 7

Here are some websites that will answer most of your questions:

http://en.wikipedia.org/wiki/Matrix_multiplication

http://www.purplemath.com/modules/mtrxmult.htm

http://people.hofstra.edu/Stefan_Waner/RealWorld/tutorialsf1/frames3_2.html

Good Luck!! Hope this helps.

Answer 8

Row and column of E and D is not equal