Basic Matrix Operations

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Basic Matrix Operations Section 6.3 Basic Matrix Operations Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

If A and B are both m × n matrices then the sum of A and B, denoted A + B, is a matrix obtained by adding corresponding entries of A and B. The difference of A and B, denoted A – B, is obtained by subtracting corresponding entries of A and B. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

The Zero Matrix Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

If A is an m × n matrix and s is a scalar, then we let kA denote the matrix obtained by multiplying every element of A by k. This procedure is called scalar multiplication. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

AB ≠ BA Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

R3= –2r1+ r3 R1= r1+ r2 R3= – 4r2+ r3 R2= –r2 R3= 1/9r3 R1= r1 + r3 R2= 3r3 + r2

R1 = –1/2r1 R2 = – 4r1 + r2 We can see that we cannot get the identity on the left side of the vertical bar. We conclude that A is singular and has no inverse. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.