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Chapter 4: Q67E (page 201)

Every three dimensional subspaceR2脳2 contains at least one invertible matrix

Short Answer

Expert verified

The given statement is True

Step by step solution

01

Determine the Subspace

Consider the given statement as follows.

The three dimensional subspace of R2脳2is defined by as follows.

abC0:a,b,c鈯�R

02

Determine if the statement is True or False

If consider that a, b and c are non-zero real numbers then the set of all matrices becomes invertible.

That isabc0=-bc鈮�0

Thus, the given statement 鈥淓very three dimensional subspace of R2脳2contains at least one invertible matrix鈥� is true.

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Most popular questions from this chapter

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphism, T(ft)=F''(t)f(t) fromP2to P2.

Find the basis of all2脳2matrix A such that [1236]A=[0000], and determine itsdimension.

Find out which of the transformations in Exercises 1 through 50 are linear. For those that are linear, determine whether they are isomorphism,T(ft)=鈭�-23f(t)dt from toP2to鈩�.

In Exercise 72through 74, let Znbe the set of all polynomials of degree鈮�nsuch that f(0) = 0.

73. Is the linear transformationT(ft)=鈭�0tf(x)dx an isomorphism fromPn-1 toZn?

if f1,f2,f3is a basis of linear space V and if f is any element of V then the elements f+f1,f+f2,f+f3must form a basis of V as well.
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