Question 16 Which of the following statements is (are) false? O All the statements are false Of the distance from u to v is the same as the distance from u to-v, then u and v are orthogonal. O For an mx matrix A, vectors in the null space of A are orthogonal to vectors in the row space of A O For any square matrix A, vectors in Col A are orthogonal to vectors to vectors in Nul A O None of the statements is false O The dot product of any two vectors in a vector space is commutative

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A: See the detailed solution below.

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A: Since you have posted multiple questions, we will provide the solutions only to the first questions…

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A: Given:

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A: To Write: v and w as linear combinations of v+w and v-w.

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A:

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A: According to our guideline we can only answer first three subparts.

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A: The given set of vectors are:To determine: The elements of  are linearly independent or not also…

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A:

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A: Definition : Null Space of a matrix A where A is m×n matrix is defined as follows x∈ℝn|Ax=0

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A: We have to write

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A:

Q: Determine

A: Length of all vectors is 1.

Q: Determine if the statements are true or false. 1. Any four vectors In R³ are linearly dependent. ?…

A: Since you have posted a multi subparts question according to guildlines I will solve first(1,2,3)…

Q: Determine whether the vector u belongs to the null space of the matrix A. Solve it on scratch. 1.

A: Here u belongs to Null(A) if and only if Au=0.

Q: SOLVE BY LINEAR METHOD - y'- 3 X Y = x 3 cos (x)

A:

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A:

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A: Let's consider the case where A and B are both 2x2 matrices. We can set up the following…