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Chapter 4: Q50E (page 200)

There exist a two dimensional subspace of R2脳2whose non-zero elements are all invertible.

Short Answer

Expert verified

The solution is the statement is true.

Step by step solution

01

Determine the two dimensional subspace

Let the two dimensional subspace of R2脳2can be defined as follows.

V={a00b|a,b鈭�R}

02

Explanation of the solution

If we take a and b are non-zero real numbers then set of all matrices becomes invertible.

That is as follows.

a00b=ab鈮�0

Therefore, the set of all non-zero two dimensionalsubspace ofR2脳2are invertible.

Thus, the given statement 鈥淭here exist a two dimensional subspace of R2脳2whose non-zero elements are invertible鈥� is true.

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Most popular questions from this chapter

Find the kernel and nullity of the transformation TinT(M)=[1201]M-M[1201]fromR(2脳2)toR(2脳2)..

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.

Find the set of all polynomial f(t)in P3 such that f(1)=0 and鈭�-11f(t)dt=0,and determine its dimension.

In Exercise 72through 74, letznbe the set of all polynomials of degree鈮�nsuch thatf(0)=0.

72. Show thatznis a subspace ofpnand find the dimension ofzn.

Consider linear transformation T from Vto Wand from Wto u. If ker T and ker L are both finite dimensional, and if im T = W,show that ker (LoT)is finite dimensional as well and that.

(ker (LoT)) = dim (Ker (T)) + dim (Ker (L))
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