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

Answer to Problem 15RE
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:
Therefore, the dimension of the matrix is
(b)
To explain: whether the matrix is in row-echelon form
(b)

Answer to Problem 15RE
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:
Therefore, the matrix is in row-echelon form
(c)
To explain: whether the matrix is in reduced row-echelon form
(c)

Answer to Problem 15RE
The matrix is not in reduced row-echelon form
Explanation of Solution
Given:
Calculation:
In reduced row-echelon form, leading
Consider the following matrix:
The leading
Hence the matrix is not in reduced row-echelon form.
Conclusion:
Therefore, the matrix is not in reduced row-echelon form
(d)
To write: the system of equations
(d)

Answer to Problem 15RE
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:
Therefore, the system of equations for which the matrix
Chapter 10 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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- r>0 (r, 0) = T 0 and one with r 0 2 (c) (9,-17) 3 (r, 8) (r, 8) r> 0 r<0 (r, 0) = (r, 8) = X X X x x Warrow_forward74. Geometry of implicit differentiation Suppose x and y are related 0. Interpret the solution of this equa- by the equation F(x, y) = tion as the set of points (x, y) that lie on the intersection of the F(x, y) with the xy-plane (z = 0). surface Z = a. Make a sketch of a surface and its intersection with the xy-plane. Give a geometric interpretation of the result that dy dx = Fx F χ y b. Explain geometrically what happens at points where F = 0. yarrow_forwardExample 3.2. Solve the following boundary value problem by ADM (Adomian decomposition) method with the boundary conditions მი მი z- = 2x²+3 дг Əz w(x, 0) = x² - 3x, θω (x, 0) = i(2x+3). ayarrow_forward
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- Officials in a certain region tend to raise the sales tax in years in which the state faces a budget deficit and then cut the tax when the state has a surplus. The graph shows the region's sales tax in recent years. Let T(x) represent the sales tax per dollar spent in year x. Find the desired limits and values, if they exist. Note that '01 represents 2001. Complete parts (a) through (e). Tax (in cents) T(X)4 8.5 8- OA. lim T(x)= cent(s) X-2007 (Type an integer or a decimal.) OB. The limit does not exist and is neither ∞ nor - ∞. Garrow_forwardDecide from the graph whether each limit exists. If a limit exists, estimate its value. (a) lim F(x) X➡-7 (b) lim F(x) X-2 (a) What is the value of the limit? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. lim F(x) = X-7 (Round to the nearest integer as needed.) OB. The limit does not exist. 17 Garrow_forwardFin lir X- a= (Us -10 OT Af(x) -10- 10arrow_forward
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