Which of the following statements is false about the given vectors?a = [1 2 3]b = [2 4 6]c = [0 1 0]d = [0 0 1]e = [4 5 6]f = [5 7 9]Select an option Clear ResponseVector a and b are linearly dependent.Vector f is a linear combination of vectors a and e.Vector a and e are linearly independent.Vector b and c are linearly dependent.
Question
Which of the following statements is false about the given vectors?a = [1 2 3]b = [2 4 6]c = [0 1 0]d = [0 0 1]e = [4 5 6]f = [5 7 9]Select an option Clear ResponseVector a and b are linearly dependent.Vector f is a linear combination of vectors a and e.Vector a and e are linearly independent.Vector b and c are linearly dependent.
Solution
The false statement is: "Vector b and c are linearly dependent."
Here's why:
-
Vector a and b are linearly dependent: This is true because vector b is a multiple of vector a. If you multiply vector a by 2, you get vector b.
-
Vector f is a linear combination of vectors a and e: This is true because if you subtract vector a from vector f, you get vector e.
-
Vector a and e are linearly independent: This is true because there is no scalar multiple or combination that can make vector a equal to vector e.
-
Vector b and c are linearly dependent: This is false because vector b is not a multiple of vector c, and there is no scalar multiple or combination that can make vector b equal to vector c.
Similar Questions
Two vectors and are given. Then which of the following options is/are correct?
Which among the statements below are correct about the vectors?i. Each vector may not have a vector representation at times.ii. Vectors can either be represented by an arrow or by component.iii. Equivalent vectors have the same magnitude and the same direction while equal vectors have the same magnitude.iv. There are two ways to perform multiplication on vectors: scalar product and vector product.Group of answer choicesi and iiiii and ivi and iiiii and iv
3. (a) If X and Y are subsets of a vector space, and either X or Y is linearly dependent, show thatX ∪ Y is linearly dependent. [6 marks](b) Give an example of a vector space V with subsets X and Y , such that X and Y are linearlyindependent, but X ∪ Y is linearly dependent.
Determine which of the following vectors are equal
Given the vector below. Which of the following statements is TRUE?Group of answer choicesThe direction of vector c is 590 South of WestThe direction of vector c is 1210 South of WestThe direction of vector c is 2390 South of WestThe direction of vector c is 310 South of West
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.