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Chapter 3: 17P (page 88)


Short Answer

Expert verified

The rank of the matrix1143311074214102064is2.

Step by step solution

01

 Step-by-Step Solution Step 1: Given information

The given matrix is.

02

 Step 2: Definition of the rank of a matrix

The number of non-zero rows remaining in a row reduced matrix is called the rank of a matrix.

03

Apply row operations to reduce the matrix into row reduction form

Consider the matrix.

Multiply row 1 by 3 and divide row 3 by

Subtract row 1 from row 2 and row 4 from row 3.

Divide row 1 by 3, row 4 by 2 and multiply row 3 by 2.

Subtract row 1 from row 4 and add row 2 to row 3.

Divide row 2 by.

Add row 4 to row 2.

The row reduced form of the given matrix is.

Here, the total number of non-zero rows is 2. Hence, the rank of the matrixis

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