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Chapter 1: Q1.3 27E (page 35)

If the rank of a 4 脳 4 matrix A is 4, what is rref(A)?

Short Answer

Expert verified

The rref(A) of a 4 x 4 matrix A with rank 4 is,1000010000100001

Step by step solution

01

Consider the system.

The number of leading 1鈥檚 in rref(A)represents the rank of a matrix A denoted byrank(A).

A is a 4 脳 4 matrix with rank 4.

02

Consider the rref of matrix.

The leading one鈥檚 of rref of a matrix represents the rank of the matrix.

As the 4 x 4 matrix A has the rank 4, thus,

rref(A)=1000010000100001

Hence, 1000010000100001 is the rref(A) of 4 x 4 matrix A with the rank 4.

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