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Chapter 3: Q51E (page 121)

Consider an n 脳 p matrix A and a p 脳m matrix B such that ker(A) = {0鈫�} and ker(B) = {0鈫�}. Find ker(AB).

Short Answer

Expert verified

ker(AB)=0鈫�

Step by step solution

01

Step 1:Objective

We know that ker(A)=0鈫� and ker(B)= 0鈫�. We want to find ker(AB)

02

Finding ker(A)=0→ and ker(B)= 0→

First if

ker(A)=0鈫�andker(B)=0鈫�thismeanstheonlysolutionstotheequationsAx鈫�=0andBx鈫�=0is0.

03

Final answer

ThustheonlysolutionstoABx鈫�=0willalsobe0鈫�makingker(AB)=0鈫�

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Most popular questions from this chapter

What is the image of a function ffrom 鈩� to 鈩�given by

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where a,b,c are arbitrary scalars?

In Exercises 21 through 25, find the reduced row-echelon form of the given matrix A. Then find a basis of the image of A and a basis of the kernel of A.

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Show that the kernels of the matrices A and B are different

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