5.andthat if I isrealLet V and W beM-dimensional IR-vector Spaces,let T and S be linear transformation from ✓ to W. Shownthere areat most hin vertible.T is invertible, thennumbersCs.t. Ttcs isnot

5. Let V and W and let T and S be linear transformation from ✓ V ^ that if T is invertible, then there are real numbers C be M-dimensional IR-vector spaces W. Show sit. T+cs is not } at most h in vertible.

5. Let V and W and let T and S be linear transformation from ✓ V ^ that if T is invertible, then there are real numbers C be M-dimensional IR-vector spaces W. Show sit. T+cs is not } at most h in vertible.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

5.
and
that if I is
real
Let V and W be
M-dimensional IR-vector Spaces,
let T and S be linear transformation from ✓ to W. Show
n
there are
at most h
in vertible.
T is invertible, then
numbers
C
s.t. Ttcs is
not

Expert Solution

Step 1: Assumption

To show that if $T$ is invertible, then there are at most $n$ real numbers $C$ such that $T + C S$ is not invertible, we can use the determinant as a tool.

Preliminaries

Let $T$ and $S$ be linear transformations from $V$ to $W$ , where $V$ and $W$ are r-dimensional $R$ -vector spaces. Assume $T$ is invertible.

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