Math 30 College Algebra April 12, 2000

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Math 30 --- College AlgebraApril 12, 2000

• Section 4.3 questions
• Section 4.2 Homework
• Break
• Section 4.4
• Assignment 25 and 26

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AnnouncementsApril 12, 2000

• Changes to the Syllabus
• 4 Exams (Exam 4 Monday 4/24
• Chapter 6 material on the Final

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Row-Equivalent Operations for Matrices
1) Interchange any two rows. 2) Multiply each
entry in a row by a nonzero constant. 3) Add a
nonzero multiple of one row to another row.
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Row-Echelon Form
1) If a row does not consist entirely of 0s,
then the first nonzero element in the row is a 1
(called a leading 1). 2) For any two successive
nonzero rows, the leading 1 in the lower row is
farther to the right than the leading 1 in the
higher row.
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Row-Echelon Form
3) All rows consisting entirely of 0s are at the
bottom of the matrix.
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Reduced Row-Echelon Forma.k.a.Gauss---Jordan
Elimination
The 3 properties of row-echelon form are
satisfied as well as 4) Each column that contains
a leading 1 has 0s everywhere else.
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Matrix Row Operations with the TI-83
1) rowSwap(matrix, rowA,rowB) 2)
row(value,matrix,row) 3) row(matrix,rowA,rowB)
row(value,matrix,rowA,rowB)
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Row-Echelon Form with the TI-83
ref(matirx)
Reduced Row-Echelon Formwith the TI-83
rref(matirx)
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Matrices
The matrix A has m rows and n columns. The order
of the A is .
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Matrix Addition and Scalar Multiplication
For any matrices A, and B, and any
scalar k
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Matrix Addition and Scalar Multiplication
For any matrices A, B, and C and any
scalars k and l
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Matrix Addition and Scalar Multiplication
For any matrix A, and any scalar k
There exists a unique matrix 0 such that
There exits a unique matrix -A such that
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Matrix Addition and Scalar Multiplication
For any matrices A and B, and any
scalars k and l
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Properties of Matrix Multiplication
For matrices A, B, and C, assuming that the
indicated operation is possible
Note In general,
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Assignment 25

• 4.2 pbs 15, 17, 19, 21, 23, 27, 29, 43
• (Set up matrix and use rref on your calculator.)
• 4.4 pbs 5, 9, 11, 13, 14, 15, 19, 20, 25, 27,
  29, 39, 41, 43, 53, 54