Q2 The Dimension of The Image and Kernel of a Linear

Transformation

50 Points

Q2.1

25 Points

Consider at linear transformation 7(@) = A@, where A c R( *8, such that

dim( ker ( A) ) = 3.

What is dim ( im ( A) ) = ?

Please select file(s)

Select file(s)

Q2.2

25 Points

Consider at linear transformation 7(@) = BE, where B C IR*, such that

dim( im (B) ) = 3.

What is dim ( ker ( B) ) = ?

Please select file(s)

Select file(s)

Q2.3 Bonus Question (20 bonus points available)

0 Points

Consider at linear transformation T(@) = Ca, such that dim ( im (C) ) = 3, and

dim ( ker (C) ) = 4.

What can we say about

(1) the number of rows of C, and

(2) the number of columns of C ?Math