cmi-entrance 2010 QB4

cmi-entrance · India · pgmath Matrices Linear Transformation and Endomorphism Properties

A linear transformation $T : \mathbb{R}^8 \rightarrow \mathbb{R}^8$ is defined on the standard basis $e_1, \ldots, e_8$ by $$\begin{aligned} & T e_j = e_{j+1} \quad j = 1, \ldots, 5 \\ & T e_6 = e_7 \\ & T e_7 = e_6 \\ & T e_8 = e_2 + e_4 + e_6 + e_8. \end{aligned}$$ What is the nullity of $T$?

A linear transformation $T : \mathbb{R}^8 \rightarrow \mathbb{R}^8$ is defined on the standard basis $e_1, \ldots, e_8$ by
$$\begin{aligned}
& T e_j = e_{j+1} \quad j = 1, \ldots, 5 \\
& T e_6 = e_7 \\
& T e_7 = e_6 \\
& T e_8 = e_2 + e_4 + e_6 + e_8.
\end{aligned}$$
What is the nullity of $T$?

Paper Questions

QA1 QA10 QA11 QA12 QA13 QA14 QA2 QA3 QA4 QA5 QA6 QA7 QA8 QA9 QB1 QB10 QB2 QB3 QB4 QB5 QB6 QB7 QB8 QB9