Find the dimension of the space $ V $ where(a) $ V $ is the space of all polynomials of degree $\leq 3$, satisfying the condition $ p(1) = 0 $.(b) $ V $ is the space of all $ (3 \times 3) $ antisymmetric real matrices.

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Find the dimension of the space V where (a) V is the space of all polynomials of degree < 3, satisfying the condition p(1) = 0. (b) V is the space of all (3 × 3) antisymmetric real matrices.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...

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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Find the dimension of the space $ V $ where

(a) $ V $ is the space of all polynomials of degree $\leq 3$, satisfying the condition $ p(1) = 0 $.

(b) $ V $ is the space of all $ (3 \times 3) $ antisymmetric real matrices.

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