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2. Consider the following system of simultaneous linear equations in five variables: a + 3b-2c+d- 6e = 12 a + 4b + 4c - 2d +5e = -1 2a +9b+2c- d - 3e = 15 3a + 13b +6c5d2e = 12 (a) Express this system in the form Av = w, where A is the coefficient matrix of the system. (b) Write down the augmented matrix A' of this system, and convert it to reduced row echelon form via a sequence of elementary row operations. (c) Calculate the rank of A and A', and use your answers to say whether the system has no solutions, a single unique solution, or multiple solutions.

2. Consider the following system of simultaneous linear equations in five variables: a + 3b-2c+d- 6e = 12 a + 4b + 4c - 2d +5e = -1 2a +9b+2c- d - 3e = 15 3a + 13b +6c5d2e = 12 (a) Express this system in the form Av = w, where A is the coefficient matrix of the system. (b) Write down the augmented matrix A' of this system, and convert it to reduced row echelon form via a sequence of elementary row operations. (c) Calculate the rank of A and A', and use your answers to say whether the system has no solutions, a single unique solution, or multiple solutions.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Consider the following system of simultaneous linear equations in five variables: a + 3b 2c + d- 6e a + 4b + 4c 2d +5e 2a +9b2c- d - 3e 3a + 13b + 6c - 5d - 2e = 12 = -1 = 15 12 = (a) Express this system in the form Av = w, where A is the coefficient matrix of the system. (b) Write down the augmented matrix A' of this system, and convert it to reduced row echelon form via a sequence of elementary row operations. (c) Calculate the rank of A and A', and use your answers to say whether the system has no solutions, a single unique solution, or multiple solutions. (d) Write down the solution set of the system of equations. (e) Find a basis for the row space of A. (f) Find a basis for the column space of A. (g) Find a basis for the kernel of A. (h) Write the vector w as a linear combination of the basis vectors in part (f).
Transcribed Image Text:2. Consider the following system of simultaneous linear equations in five variables: a + 3b 2c + d- 6e a + 4b + 4c 2d +5e 2a +9b2c- d - 3e 3a + 13b + 6c - 5d - 2e = 12 = -1 = 15 12 = (a) Express this system in the form Av = w, where A is the coefficient matrix of the system. (b) Write down the augmented matrix A' of this system, and convert it to reduced row echelon form via a sequence of elementary row operations. (c) Calculate the rank of A and A', and use your answers to say whether the system has no solutions, a single unique solution, or multiple solutions. (d) Write down the solution set of the system of equations. (e) Find a basis for the row space of A. (f) Find a basis for the column space of A. (g) Find a basis for the kernel of A. (h) Write the vector w as a linear combination of the basis vectors in part (f).
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