Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.

No, thanks

6.3 Matrix Operations and Applications

Students will be able to add, subtract, and multiply matrices by a scalar and be able to organize data using matrices.
by

Justine Anders

on 7 September 2012

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of 6.3 Matrix Operations and Applications

6.3 Matrix Operations and Their Applications You will be able to add, subtract, and multiply matrices by a scalar, as well as be able organize data. Notations for Matrices Denoted by a capitalized letter like A, B, or C.
A lowercase letter is inclosed in brackets denotes a matrix.
A=[a ] . i is the ith row and j is the jth column
The order: like RC Cola- Rows then Columns
A matrix of order m x n has m rows and n columns. Matrix Notation A = Example Time What is the order of A?
Identify a and a Two matrices A and B are equal if and only if they have the same order m x n and a =b for i=1,2,....m and j=1,2,.....m Equality of Matrices A =

B=

A= B if and only if x=1, y+1=5, and z=3 Need to have the same order m x n to add and subtract

Matrix addition is very simple; we just add the corresponding elements.

Example 1:



Example 2: Matrix Addition and Subtraction Add or Subtract the Following Matrices Your turn to Practice Multiply each element of the Matrix A by the scalar c. Multiplying by a Scalar Any matrix with all zero entries for the elements is called a zero matrix.

Examples: Properties of Matrix Addition This is called the
Additive Identity Commutative Property of Addition: 3 + 4 = 4 + 3
Associative Property of Addition: (3+4) + 5 = 3 + (4+5)
Additive Identity: 3 + 0 = 0 + 3 = 3
Additive Inverse: 3 + (-3) = (-3) + 3 = 0 Determine if the Commutative Property of Addition, Associative Property of Addition, Additive Identity, and Additive Inverse Properties of Real Numbers hold true for Matrices. If A =

and B=
find -5B and 2A + 3B Example: Associative Property of Addition:
Commutative Property of Addition:
Distributive Property: Review Properties of Real Numbers What would these properties look like for matrices? Associative Property of Scalar Multiplication
(cd)A= c(dA)
Scalar Identity Property
1A = A
Distributive Property
c(A + B) = cA + cB
Distributive Property
(c + d)A = cA + dA Solve for X in the matrix equation 2X + A = B
where A = and B = Solving a Matrix Equation -1 5
0 2 -6 5
9 1 -1 4
3 0 2 -3
5 -6 0 5 3
-2 6 -8 + -2 4 5
7 -9 6 -6 7
2 -3 - -5 6
0 -4 23 12 ij Perform the indicated operations to answer the following questions CLOSURE 5 -2
-3 4
1 6 A= What is the order of A?
Identify a and a 12 31 If A= and B=
find -6B and 3A + 2B -4 1
3 0 -1 -2
8 5 -4 3
7 -6 + 6 -3
2 -4 5 4
-3 7
0 1 -4 8
6 0
-5 3 - 3 2 0
-4 5 -1/5 x y+1
z 6 1 5
3 6 1 2 -5 2
3 6 0 0
0 0 + = -5 2
3 6 REVIEW
Full transcript