CONTINUATION ...
Elementary
Row Operations
1. Interchange two rows
2. Multiply a row by a nonzero constant
3. Add a multiple of a row to another row
Two matrices
are said to be Row Equivalent of one can be
obtained from the other by a finite sequence of elementary row operations
Definition of Row Echelon Form of a Matrix
1. All rows consisting entirely of zeros occur at the bottom of the matrix
2. For each row that does not consist entirely of zeros the first nonzero entry
is
3. For two successive (nonzero) rows the leading 1 in the higher row is farther
to the left that the leading 1 in the lower row
A Homogeneous
System is a system of
linear equations in which each of the constant terms is zero
A homogeneous system must have at least one solution. A
solution in which all of the variables have the value zero is called trivial or obvious.
1. Interchange two rows
2. Multiply a row by a nonzero constant
3. Add a multiple of a row to another row
Two matrices
are said to be Row Equivalent of one can be
obtained from the other by a finite sequence of elementary row operations
Definition of Row Echelon Form of a Matrix
1. All rows consisting entirely of zeros occur at the bottom of the matrix
2. For each row that does not consist entirely of zeros the first nonzero entry is
3. For two successive (nonzero) rows the leading 1 in the higher row is farther to the left that the leading 1 in the lower row
1. All rows consisting entirely of zeros occur at the bottom of the matrix
2. For each row that does not consist entirely of zeros the first nonzero entry is
3. For two successive (nonzero) rows the leading 1 in the higher row is farther to the left that the leading 1 in the lower row
A Homogeneous
System is a system of
linear equations in which each of the constant terms is zero
A homogeneous system must have at least one solution. A
solution in which all of the variables have the value zero is called trivial or obvious.
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''People who don’t work hard don’t have the right
to be envious of the people with talent. People fail because they don’t
understand the hard work necessary to be successful.''
~ Yukino Yukinoshita (My Teen Romantic Comedy
Snafu)
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