MATRIX SCALAR MATH

REVISED: Sunday, March 3, 2013

You will learn Matrix Scalar Math.

I.  MATRIX ADDITION

Shown below are two matrices, A and B.

  A          B
1  2      1  2
3  4      3  4
5  6      5  6

You can only add two matrices of the same dimension.

The above example is two 3x2 matrices; therefore, we can add them as follows:

(1+1)    (2+2)
(3+3)    (4+4)
(5+5)    (6+6)

Notice when we add them, the result is a new 3x2 matrix as follows:

         C
  2       4
  6       8
10     12

II.  MULTIPLYING A MATRIX BY A SCALAR NUMBER

Scalar means real number.

For example lets multiply the following 3x2 matrix C by the scalar, real number, 3.

       C
  2       4
  6       8
10     12

and our 3x2 product is as follows:

              C
  (3*2)      (3*4)
  (3*6 )     (3*8)
(3*10)    (3*12)

which becomes:

       C
   6      12
 18      24
 30      36

Notice the above result is a matrix of the same 3x2 dimensions.

III.  DIVIDING A MATRIX BY A SCALAR NUMBER

Lets divide the following 3x2 matrix C by the scalar, real number, 3.

We can achieve the same results of division by 3, by multiplication by the inverse of 3, which is 1/3.

We already know how to multiply a matrix by a scalar so we are all set.

Lets multiply the following 3x2 matrix C by the scalar, real number, 1/3.

       C
  6       12
 18      24
 30      36

becomes:
                       C
  (1/3 *  6 )     (1/3 * 12)
 (1/3 * 18)      (1/3 * 24)
 (1/3 * 30)      (1/3 * 36)

which is:

       C
  2       4
  6       8
10     12

IV.  COMBINATION OF OPERANDS

Shown below are three, 3x1 matrices, or vectors.
We want to multiply the scalar number 2, times vector a.
We want to divide vector c , by the scalar number 3.
Then we want to add vectors (a + b), and subtract vector c.

        a    b    c
        1      2      3
2 *   4  +  5  -   6   / 3
        7      8      9

becomes

        a       b      c
    (2 * 1)      2      (3*1/3)
    (2 * 4)  +  5  -   (6*1/3)
    (2 * 7)      8      (9*1/3)

becomes

        a    b      c
        2      2      (3*1/3)
        8  +  5  -   (6*1/3)
      14      8      (9*1/3)

becomes

        a    b    c
        2      2      1
        8  +  5  -   2
      14      8      3

becomes

         a   b     c

        (2 + 2)      1
        (8 + 5)  -   2
      (14 + 8)      3

becomes

               c
         4      1
       12  -   2
       22      3

becomes

               c
         (4  -  1)
       (12  -  2)
       (22  -  3)

becomes vector 3x1 d.

               d
                 3
               10
               19

You have learned Matrix Scalar Math.

Elcric Otto Circle

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