Explanation Given: The matrix are A = [ 1 1 − 1 5 0 2 − 1 7 4 2 − 3 13 ] and b = [ 0 0 0 ] . The form (4.9.3) is, x = c 1 x 1 + c 2 x 2 + ... + c n − r x n − r + x p Here, x p is any particular solution to A x = b and { x 1 , x 2 ... x n − r } is a basis for null space ( A ) . Approach: The Augmented matrix of A x = b is given by, A # = [ a d g j 0 b e h k 0 c f i l 0 ] Here, n is the number of column and N is the nullity. The number of non zero number in row-echelon form is equal the rank of matrix. Calculation: Write the augmented matrix of the given matrix. [ 1 1 − 1 5 0 0 2 − 1 7 0 4 2 − 3 13 0 ] Apply the operation R 3 = R 3 − ( 1 ) R 1 . [ 1 1 − 1 5 0 0 2 − 1 7 0 0 − 2 1 − 7 0 ] Apply the operation R 3 = R 3 + ( 1 ) R 1 . [ 1 1 − 1 5 0 0 2 − 1 7 0 0 0 0 0 0 ] Rewrite the above matrix in system of equations. w + x − y + 5 z = 0 ... ( 1 ) . 2 x − y + 7 z = 0 ... ( 2 ) . Suppose z = t 1 , y = t 2 Here, t 1 , t 2 are free variables

Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition)

4th Edition

ISBN: 9780321985811

Author: Stephen W. Goode, Scott A. Annin

Publisher: Pearson (edition 4)

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Chapter 4.9, Problem 13P

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The solution set to Ax=b, and it is to be shown that solution is in the form of x=c1x1+c2x2+...+cn−rxn−r

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Chapter 4.9, Problem 12P

Chapter 4.9, Problem 14P

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Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition)

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The solution set to A x = b , and it is to be shown that solution is in the form of x = c 1 x 1 + c 2 x 2 + ... + c n − r x n − r

Solution Summary: The author explains that the Augmented matrix of Ax=b is given by A#=left.

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To find:

The solution set to Ax=b, and it is to be shown that solution is in the form of x=c1x1+c2x2+...+cn−rxn−r

Want to see the full answer?

Chapter 4 Solutions

The solution set to A x = b , and it is to be shown that solution is in the form of x = c 1 x 1 + c 2 x 2 + ... + c n − r x n − r

Solution Summary: The author explains that the Augmented matrix of Ax=b is given by A#=left.

Concept explainers

Videos

To find: The solution set to Ax=b, and it is to be shown that solution is in the form of x=c1x1+c2x2+...+cn−rxn−r

Want to see the full answer?

Chapter 4 Solutions

To find:

The solution set to Ax=b, and it is to be shown that solution is in the form of x=c1x1+c2x2+...+cn−rxn−r