Understanding Vector Spaces and Linear Combinations

The video tutorial explains vector space P2, which includes polynomials of degree at most 2 and the zero polynomial. It covers the properties of vector spaces, such as addition and scalar multiplication. The tutorial demonstrates how to calculate a linear combination of vectors and find the additive inverse of a vector within this space.

What is the expression for vector A in vector space P2?

• 4t^2 - 3t + 1

• 2 - 6x - 2x^2

• 5 - t^2

• 3 + t + 4t^2

Which of the following is NOT a property of vector space P2?

• Existence of additive inverses

• Existence of additive identity

• Non-commutative multiplication

• Closure under addition

How do you express the linear combination -3A - B?

• -3(3 + t + 4t^2) - (-5 - t^2)

• -3(5 - t^2) - (3 + t + 4t^2)

• -3(2 - 6x - 2x^2) - (5 - t^2)

• -3(4t^2 - 3t + 1) - (2 - 6x - 2x^2)

What is the result of combining like terms in the expression -9 - 3t - 12t^2 + 5 + t^2?

• -4 + 3t + 11t^2

• -4 - 3t - 11t^2

• -4 - 3t + 11t^2

• -4 + 3t - 11t^2

What is the additive inverse of the polynomial 2 - 6x - 2x^2?

• -2 - 6x - 2x^2

• 2 - 6x + 2x^2

• 2 + 6x + 2x^2

• -2 + 6x + 2x^2