A6S - ASSIGNMENT 6 Solutions Let n be odd and T R n R n be...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ASSIGNMENT 6 Solutions Let n be odd, and T : R n R n be the linear transformation given by T : x 1 x 2 x 3 . . . x n- 1 x n 7 x 1 + x 2 x 2 + x 3 x 3 + x 4 . . . x n- 1 + x n x n + x 1 1. [4 marks] Find the standard matrix, kernel and range of T . Let e i denote the i th column of the n n identity matrix. Then the standard matrix of T is A = T ( e 1 ) T ( e n ) = 1 1 1 1 1 . . . . . . . . . . . . . . . . . . . . . 1 1 1 1 1 1 . This matrix is invertible. Taking the determinant along the 1 st column, we get det A = det 1 1 1 . . . . . . . . . . . . . . . . . . 1 1 1 1 1 + (- 1) n +1 det 1 1 1 ....
View Full Document

{[ snackBarMessage ]}

Page1 / 3

A6S - ASSIGNMENT 6 Solutions Let n be odd and T R n R n be...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online