Homework Answers
Add Answer to:
Let A be an nx n matrix. Select all of the following that are equivalent to...
8. Let A be a 5 x 4 matrix such that its reduced row echelon form...
8. Let A be a 5 x 4 matrix such that its reduced row echelon form has 4 pivot positions (leading entries). Which of the following statements is TRUE? a) The linear transformation T : R4 → R5 defined by T(X) = AX is onto. b) AX = 0 has a unique solution. c) Columns of A are linearly dependent. d) AX b is consistent for every vector b in R
A.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero mat...
a.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero matrix b.) The row echelon form of an invertible 3 * 3 matrix is invertible c.) If A is an m*n matrix and the equation Ax=0 has only the trivial solution, then the columns of A are linearly independent. d.) If T is the linear transformation whose standard matrix is an m*n matrix A and the...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set o...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
12. Which of the following is NOT equivalent to the n xn matrix A being invertible?...
12. Which of the following is NOT equivalent to the n xn matrix A being invertible? A. The homogeneous system associated to A has a unique solution. B. Some non-homogeneous system whose coefficient matrix is A has a unique solution. C. Every non-homogeneous system whose coefficient matrix is A is consistent. D. The column space of A is R". E. The linear transformation xH Ax is one-to-one.
Write each statement as True or False (a) If an (nx n) matrix A is not invertible then the linear system Ax-O hns infinitely many b) If the number of equations in a linear system exceeds the number o...
Write each statement as True or False (a) If an (nx n) matrix A is not invertible then the linear system Ax-O hns infinitely many b) If the number of equations in a linear system exceeds the number of unknowns then the system 10p solutions must be inconsistent ) If each equation in a consistent system is multiplied through by a constant c then all solutions to the new system can be obtained by multiplying the solutions to the original...
5. This problem is to help you relate many of the topics we have discussed this semester. Fill in the blanks Let A be an n × n matrix. A is nonsingular if and only if (a) The homogeneous linear syste...
5. This problem is to help you relate many of the topics we have discussed this semester. Fill in the blanks Let A be an n × n matrix. A is nonsingular if and only if (a) The homogeneous linear system A0 has b) A is row equivalent to (c) The rank of A is (d) Theof A are linearly independent (e) Theof A span (f) The (g) N(A) = of R" Of A form a (i) The map V...
Linear Algebra Please list whether the following is True or False: (16) Let A be an...
Linear Algebra
Please list whether the following is True or
False:
(16) Let A be an m × n matrix. If each column of A has a pivot, then the columns of A can span Rn (17) (AB)T ATBT (18) The product of two diagonal matrices of the same size is a diagonal matrix (19) If AB- AC, then B- C. (20) Every matrix is row equivalent to a unique matrix in row reduced echelon form
12. a. If there is an n x n matrix D such that AD = 1,...
12. a. If there is an n x n matrix D such that AD = 1, then there is also an n x n matrix C such that CA= 1. b. If the columns of A are linearly independent, then the columns of A span Rn. c. If the equation Ax = b has at least one solution for each bin Rn, then the solution is unique for each b. d. If the linear transformation (x) -> Ax maps Rn into Rn, then...
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer....
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 0 3 - 4 0 2 -4 -9 4 Choose the correct answer below. O A. The matrix is not invertible. If the given matrix is A, the equation Ax=b has at least one solution for each b in R3. OB. The matrix is invertible. The given matrix has 3 pivot positions. C. The matrix is invertible. The columns of the given matrix span...
i need help with these two questions. it is from linear algebra Describe the possible echelon...
i need help with these two
questions. it is from linear algebra
Describe the possible echelon forms of the following matrix. A is a 2x2 matrix with linearly dependent columns. Select all that apply. (Note that leading entries marked with an X may have any nonzero value and starred entries may have any value including zero.) A. Х * B. 0 X 0 0 0 X C. х * D. 0 0 0 0 0 1 5 4 -5 -8...
8. Let A be a 5 x 4 matrix such that its reduced row echelon form has 4 pivot positions (leading entries). Which of the following statements is TRUE? a) The linear transformation T : R4 → R5 defined by T(X) = AX is onto. b) AX = 0 has a unique solution. c) Columns of A are linearly dependent. d) AX b is consistent for every vector b in R
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
12. Which of the following is NOT equivalent to the n xn matrix A being invertible? A. The homogeneous system associated to A has a unique solution. B. Some non-homogeneous system whose coefficient matrix is A has a unique solution. C. Every non-homogeneous system whose coefficient matrix is A is consistent. D. The column space of A is R". E. The linear transformation xH Ax is one-to-one.
Write each statement as True or False (a) If an (nx n) matrix A is not invertible then the linear system Ax-O hns infinitely many b) If the number of equations in a linear system exceeds the number of unknowns then the system 10p solutions must be inconsistent ) If each equation in a consistent system is multiplied through by a constant c then all solutions to the new system can be obtained by multiplying the solutions to the original...
5. This problem is to help you relate many of the topics we have discussed this semester. Fill in the blanks Let A be an n × n matrix. A is nonsingular if and only if (a) The homogeneous linear system A0 has b) A is row equivalent to (c) The rank of A is (d) Theof A are linearly independent (e) Theof A span (f) The (g) N(A) = of R" Of A form a (i) The map V...
Linear Algebra
Please list whether the following is True or
False:
(16) Let A be an m × n matrix. If each column of A has a pivot, then the columns of A can span Rn (17) (AB)T ATBT (18) The product of two diagonal matrices of the same size is a diagonal matrix (19) If AB- AC, then B- C. (20) Every matrix is row equivalent to a unique matrix in row reduced echelon form
Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answer. 0 3 - 4 0 2 -4 -9 4 Choose the correct answer below. O A. The matrix is not invertible. If the given matrix is A, the equation Ax=b has at least one solution for each b in R3. OB. The matrix is invertible. The given matrix has 3 pivot positions. C. The matrix is invertible. The columns of the given matrix span...
i need help with these two
questions. it is from linear algebra
Describe the possible echelon forms of the following matrix. A is a 2x2 matrix with linearly dependent columns. Select all that apply. (Note that leading entries marked with an X may have any nonzero value and starred entries may have any value including zero.) A. Х * B. 0 X 0 0 0 X C. х * D. 0 0 0 0 0 1 5 4 -5 -8...
Most questions answered within 3 hours.
-
Suppose that on a temperature scale X, water boils at 203.0°X
and freezes at -105.7°X. What...
asked 17 minutes ago -
BaS crystallizes in a cubic unit cell with S2- ions on each
corner and each face....
asked 48 minutes ago -
A. 0≤P(Oi)≤10≤P(Oi)≤1 for each i
B. P(Oi)≤0P(Oi)≤0
C. P(Oi)=1+P(OCi)P(Oi)=1+P(OiC)
D. P(Oi)≥1P(Oi)≥1
If an experiment consists of...
asked 2 hours ago -
A battery has an emf of 9.20V and an internal resistance of 1.20
ohm. a)What resistance...
asked 2 hours ago -
The area of an elastic circular loop decreases at a constant
rate, dA/dt = −6.60×10−3 m2/s...
asked 3 hours ago -
The denaturation of proteins can be described by the
equilibrium
F⇌U
where F and U represent...
asked 4 hours ago -
Please answer what the maximum and minimum force is, and the
angle on the ion is...
asked 4 hours ago -
implement a program that reads a number of rows and a symbol.
The program will draw...
asked 5 hours ago -
Assume that when adults with smartphones are randomly selected,
45% use them in meetings or classes....
asked 5 hours ago -
Determine the number of formula units of
Na2SO4 and moles of oxygen contained in 8.11
moles...
asked 5 hours ago -
Explain in steps on the following code
What would be the output when executed
using System;...
asked 5 hours ago -
Given the information in the table, which of the following
statements is CORRECT?
Stock A
Stock...
asked 5 hours ago