Consider the matrix 5 − 9 − 57 1 − 2 − 12 . Identify two row operations that could be used to obtain a leading entry of 1 in the first row. Also indicate which operation would be less cumbersome as a first step toward writing the matrix in reduced row-echelon form.
Consider the matrix 5 − 9 − 57 1 − 2 − 12 . Identify two row operations that could be used to obtain a leading entry of 1 in the first row. Also indicate which operation would be less cumbersome as a first step toward writing the matrix in reduced row-echelon form.
Solution Summary: The author explains the two row operations that could be used to obtain a leading entry of 1 in first row in the matrix.
Consider the matrix
5
−
9
−
57
1
−
2
−
12
.
Identify two row operations that could be used to obtain a leading entry of
1
in the first row. Also indicate which operation would be less cumbersome as a first step toward writing the matrix in reduced row-echelon form.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
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