Determine if the statements are true or false. 1. Any four vectors in R3 are linearly dependent. ? 2. Any four vectors in R³ span R³ ? 3. The rank of a matrix is equal to the number of pivots in its RREF. ? 4. {V₁, V2,..., Vn} is a basis for span(V₁, V2,..., Vn). ? 5. If v is an eigenvector of a matrix A, then v is an eigenvector of A+ cI for all scalars c. (Here I denotes the identity matrix of the same dimension as A.) ? 6. An n x n matrix A is diagonalizable if and only if it has n distinct eigenvalues. ? 7. Let W be a subspace of R". If p is the projection of b onto W, then b-pEW¹ ? Note: You can earn partial credit on this problem. V

Q: can you explain the first few questions aswell

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Q: the true answer is $

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Q: parts iv and v please

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Q: 1. O O O O lim (In(x))* ? 5.

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Q: 3. H-8)- (4-8) -10

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Q: -3 1 8 3 7 -1 4 0 5 3]

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Q: 3-3+1=?

A: NOTE As you don't mention what to find. I am just simplify the expression.

Q: Since this is a second question, can you answer the other 2 sub parts

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Q: what about questions 4-15?

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Q: D) lim f(x)=| 23 E) lim → 8 f(x) = F) lim f(x)= z 2

A: D) we know that, limx→3f(x)=limx→3+f(x)=limx→3-f(x)But limx→3+f(x)=2limx→3-f(x)=-1Since…

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Q: 7 -18 -2 -3 A = 3 P = -8 -1 -1

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Q: A3,3=? 2 6 9 3 4 1 7 7 8

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Q: 1 -3 -27 A =| -2 7 -2 5. 54

A: The given matrix is: A=1-3-2-275-254 Find the inverse of the matrix: Formula: A-1=1AAdj A, where Adj…

Q: Can someone explain how I do numbers 1 and 2 A and B.

A: (1)  The weather report get to know about that from the past experiences. For example in the similar…