
(a)
To state: the dimension of the matrix.
(a)

Answer to Problem 16RE
The dimension of the matrix is
Explanation of Solution
Given:
Calculation:
Consider the following matrix:
The dimension of a matrix is given by
In matrix
Number of columns,
Thus, the dimension of the matrix is
Conclusion:
The dimension of the matrix is
(b)
To explain: whether the matrix is in row-echelon form
(b)

Answer to Problem 16RE
The matrix is in row-echelon form
Explanation of Solution
Given:
Calculation:
A matrix that satisfies the following conditions is said to be in row-echelon form:
(1) In each row, the first non-zero number should be
(2) The leading entry in each row is to the right of that in the row immediately above it
(3) Rows whose elements are all zeros are at the bottom of the matrix
(4) All elements above and below the leading entry are
The first three conditions should be satisfied for the matrix to be in row-echelon form and if the fourth condition is also satisfied then the matrix is in reduced row-echelon form.
Consider the following matrix:
As the first non-zero number is
The leading entry in the second row is to the right of that in first row. Hence the second condition is satisfied.
There are no rows whose all elements are zeros.
Hence the matrix is in row-echelon form.
Conclusion:
The matrix is in row-echelon form
(c)
To state: whether the matrix is in reduced row-echelon form
(c)

Answer to Problem 16RE
The matrix is in reduced row-echelon form
Explanation of Solution
Given:
Calculation:
In reduced row-echelon form, leading
Consider the following matrix:
The two leading
Hence the matrix is in reduced row-echelon form.
Conclusion:
Therefore, the matrix is in reduced row-echelon form
(d)
To write: the system of equations
(d)

Answer to Problem 16RE
The system of equations for which the matrix
Explanation of Solution
Given:
Calculation:
Consider the following matrix:
Augmented matrix consists of the coefficients and constants of the system of equations.
Thus, the system of equations for which the matrix
Conclusion:
The system of equations for which the matrix
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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