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Chapter 4: Q5E (page 199)

State true or false, the spaceR2脳3is five-dimensional.

Short Answer

Expert verified

False.

Step by step solution

01

Consider the statement below.

SpaceR2脳3 is space of all 2脳3matrices and it is six dimensional.

Space R2脳3have a basis,

Since dimension of space is equal to number of base elements, then,

Dim R2脳3=6

Hence, the statement is false.

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Most popular questions from this chapter

Let Vbe the space of all infinite sequences of real numbers. See Example 5. Which of the subsets of Vgiven in Exercises 12 through 15 are subspaces of V? The square-summable sequences(x0,x1,...) (i.e., those for which鈭�i=0鈭�xi2converges).

Find the basis of all nxn diagonal matrix, and determine its dimension.

Show that in an n-dimensional linear space we can find at most n linearly independent elements.

In Exercises 5 through 40, find the matrix of the given linear transformationwith respect to the given basis. If no basis is specified, use standard basis:渭=(1,t,t)forP2,

role="math" localid="1659423247247" 渭=([1000],[0100],[0010],[0001])

for2脳2androle="math" localid="1659421462939" 渭=(1,i)for,.For the spaceU2脳2of upper triangular2脳2matrices, use the basis

渭=([1000],[0100],[0001])

Unless another basis is given. In each case, determine whether Tis an isomorphism. If Tisn鈥檛 an isomorphism, find bases of the kernel and image of Tand thus determine the rank of T.

12. T(M)=M[2003]fromR2脳2toR2脳2.

TRUE OR FALSE?

4. The kernel of a linear transformation is a subspace of the domain.
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