Linear Transformations and Their Properties

The video tutorial explains linear transformations, focusing on calculating T of u and T of negative u using properties of linear transformations. It demonstrates how to find T of the difference of 5u and 6v by applying these properties, including factoring and vector addition. The tutorial concludes with a summary of the calculations and their results.

What are the given values for T(u) and T(v) in the linear transformation?

• T(u) = (5, 2) and T(v) = (-5, 2)

• T(u) = (2, 5) and T(v) = (2, -5)

• T(u) = (-5, 2) and T(v) = (5, 2)

• T(u) = (5, -2) and T(v) = (-5, -2)

How can T(-u) be expressed using the properties of linear transformations?

• T(-u) = T(u) - 1

• T(-u) = 1 * T(u)

• T(-u) = T(u) + 1

• T(-u) = -1 * T(u)

What is the result of T(-u) when T(u) = (5, 2)?

• (-5, -2)

• (5, -2)

• (-5, 2)

• (5, 2)

How is T(5u - 6v) initially expressed using linear transformation properties?

• T(5u - 6v) = T(5u) + T(6v)

• T(5u - 6v) = T(5u) + T(-6v)

• T(5u - 6v) = T(-5u) + T(6v)

• T(5u - 6v) = T(5u) - T(6v)

What is the expression for T(5u) using the properties of linear transformations?

• 5 * T(u)

• T(u) + 5

• 5 + T(u)

• T(u) - 5

What is the expression for T(-6v) using the properties of linear transformations?

• -6 * T(v)

• T(v) - 6

• 6 * T(v)

• T(v) + 6

What is the result of multiplying 5 with T(u) when T(u) = (5, 2)?

• (25, 10)

• (10, 25)

• (5, 10)

• (10, 5)

What is the result of multiplying -6 with T(v) when T(v) = (-5, 2)?

• (-30, 12)

• (12, -30)

• (-12, 30)

• (30, -12)

What is the final result of the transformation T(5u - 6v)?

• (50, 2)

• (50, -2)

• (55, -2)

• (55, 2)