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Chapter 1: Q17E (page 1)

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

17: Rank|222222222|=2.

Short Answer

Expert verified

Answer:

False, Rank of 222222222=1.

Step by step solution

01

Rank of matrix 

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

We have given the matrix.

222222222

02

Justification of answer  

Now, reduce the given matrix into row echelon form.

222222222R2鈫�R2-R1R3鈫�R3-R1~222222222

Now, the given matrix is in echelon form. Thus, the number of non-zero rows is equal to the rank of the matrix is 1.

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Most popular questions from this chapter

In exercises 1 through 10, find all solutions of the linear systems using elimination. Then check your solutions

7. x+2y+3z=1x+3y+4z=3x+4y+5z=4

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

20:Vector [123] is a linear combination of [456]and[789] .

Balancing a chemical reaction. Consider the chemical reaction

aNO2+bH2O鈫�cHNO2+dHNO3,

where a, b, c, and d are unknown positive integers. The reaction must be balanced; that is, the number of atoms of each element must be the same before and after the reaction. For example, because the number of oxygen atoms must remain the same,

2a+b=2c+3d.

While there are many possible values for a,b,c and d that balance the reaction, it is customary to use the smallest possible positive integers. Balance this reaction.

If A is a non-zero matrix of the form [a-bba],then the rank of A must be 2.

Compute the products Ax in Exercises 16 through 19

using paper and pencil (if the products are defined).

17.


[123456].[78]
See all solutions

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