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Linear Algebra and its Applications
Found in: Page 39
Linear Algebra and its Applications

Linear Algebra and its Applications

Book edition 5th
Author(s) David C. Lay, Steven R. Lay and Judi J. McDonald
Pages 483 pages
ISBN 978-03219822384

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Short Answer

Question: Determine whether the statements that follow are true or false, and justify your answer.

14: rank .|111123136|=3


True, rank of the given matrix is 3 because after finding the row echelon form there are three non-zero rows.

See the step by step solution

Step by Step Solution

Step 1: Rank of a matrix

For finding the rank of the matrix first of all we will change the given matrix in the echelon form.

We have given the matrix.


Step 2: Justification of answer

Now, find the reduced row echelon form of the given system.


Now, the given matrix is in echelon form. Thus, the number of non-zero rows is equal to the rank of a matrix.

Thus, the rank of a matrix is 3.

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