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Chapter 4: Q1E (page 199)

TRUE OR FALSE?

  1. The polynomial of degree less than 7 form a seven dimensional subspace of the linear space of all polynomials.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Definition of a polynomial.

A polynomial is the sum or difference of a collection of algebraic terms.

For example,

An algebraic expression of the form

anxn+an-1xn-1+......+a2x2+a1x+a0

  • Where all coefficientsare real numbers.
  • an鈮�0
  • The degreen is a non-negative integer.
02

Explanation for the given statement

Polynomials of degree less than seven form a spacep6 of all polynomials of degree six or less.

So, generally dimension of n+1 space of polynomials of degree 7 or less in n+1 to account for zero-degree polynomials.

Hence, the statement is true.

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Most popular questions from this chapter

Show that if 0 is the neutral element of a linear space V then k0=0, for all scalars k.

TRUE OR FALSE?

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