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Material Type: Exam; Class: MATH 1630: If high school precalculus and ACT math of at least 21 contact 694-6450.; Subject: Mathematics; University: Pellissippi State Technical Community College; Term: Unknown 1989;
Typology: Exams
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A linear system such as can be solved by hand algebraically or by using an
x 5y z 11
3z 12
2x 4y 2z 8
augmented matrix and elementary row operations.
A. Elementary row operations that produce row-equivalent matrices
i j
i i
kR →R
j i i
kR + R →R
(NOTE : →means "replaces")
II. Performing elementary row operations on the TI-
The result of a row operation is displayed on the home screen, but it is not automatically stored!
You should immediately store the result under a different name. It is convenient (and frequently
useful) to store the results alphabetically.
A. Row swap
To interchange rows 1 and 3 of matrix A:
MATRIX MATH C:rowSwap( ENTER MATRIX
B. Multiplying a row by a nonzero scalar
To multiply row 1 of matrix A by :
MATH E:*row( MATRIX ENTER
C. Adding a nonzero scalar multiple of one row to another row
To multiply row 2 of matrix A by and add it to row 3
(of matrix A):
MATH F:*row+(
MATRIX ENTER
III. Solve the system of equations represented by the given augmented matrix using the given row
operations:
As you perform each row operation, record the result, and store it as indicated.
Let [A] =
matrix operation result store as matrix
1 3
1 2 2
2 2
2 1 1
3 3
3 1 1
The solution (x, y, z) should be in the column to the right of the bar. (x, y, z) = _____________
IV. This system could have been solved using different row operations and/or the same row operations
in other orders. To minimize the amount of work necessary to solve the system, you must be
careful not to backtrack and “undo” work which you have already done. The process we have been