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Q89E

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Linear Algebra With Applications

Found in: Page 147

Book edition 5th

Author(s) Otto Bretscher

Pages 442 pages

ISBN 9780321796974

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Short Answer

Suppose a matrix A in reduced row-echelon form can be obtained from a matrix M by a sequence of elementary row operations. Show that $A = r r e f (M)$ . Hint: Both A and $r r e f (M)$ are in reduced row-echelon form, and they have the same kernel. Exercise 88 is helpful.

Thus, it is proved that $A = r r e f (M)$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given in the question.

Both A and $r r e f (M)$ are in reduced row-echelon form, and they have the same kernel.

Step 2: Prove that A=rref(M).

Suppose A is in reduced row –echelon form which is obtained from a matrix M by a sequence of elementary row operations.

Now, since both A and $r r e f (M)$ are reduced row-echelon form.

Therefore, they are the same matrices such that $k e r A = k e r (r r e f (M))$ .

Thus, the matrices are same.

Hence, it is proved that $A = r r e f (M)$ .

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