Let 1 0 1 2 3 3 A = -( : )--( * = 0 1 1 02 B = 0 1 1 02 ● 000 00 0 0 1 0 1 Which of the following statements is true? 1012 The nullspace of A is contained in the nullspace of B. The nullspace of B is contained in the nullspace of A. The only common element of both nullspaces is the all-zero vector. The nullspace of A is equal to the nullspace of B.

Q: 2 Consider the bases B₁ and B₂. 2 -3 -7 4 {{³][])} {₁ 6 -5 B₁ = Find [x]B₂ if [x]B₁ 2 [²]. 6

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A: (a) Find u→+v→ as follows: u→+v→=-1,2,4+-3,5,2          =-1+-3,2+5,4+2          =-4,7,6

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A: Given B has a column of zeros , then to find BA has a column of zero or not .

Q: -5 7 Eхample 61. Find the adjoint of A = -2 and show that A (adj. A)=|A| I.

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Q: 25. Show that |v|u + Ju|v and |v|u – |u| v are orthogonal.

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A: Use the results and roperties of diagonalization of matrix to solve this problem.

Q: a= b= C= id=

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A: To verify is the given matrix A is invertible Or not.

Q: show all th work with correct ans

A: Solution attached.Explanation:Step 1:Step 2:Step 3:Step 4:

Q: 5. Show that the set of complex numbers can be considered a vector space over the set of real…

A: A Complex number is in the form x + yi where x , y are real numbers and i is an imaginary number.…

Q: 9. Assume that the stated inverses exist, prove (A+ B)-1 = A-'(A-1+B-!)-'B-1.

A: Here we prove a equivalent statement.

Q: Let A: = -7 2 6 -4 -1 - 9 6 5 7 5-8 3 Find a nonzero vector v in Col(A).

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Q: Please note that a bold letter indicates a vector and that this problem involves a vector function…

A: Function is given as,

Q: Find bases for the null and range spaces of 1 2 3 1 1 1 A = 3 4 5

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Q: 10 8- A 6- 2 -10-86 246 8 10 B -8 MathBits.com -10

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Q: Show that the complex numbers 2 + 3i and 1 – 2i generate the vector space

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Q: 2. a. In each part express the vector as a linear combination of 2+x+4x², p₂ = 1 − x + 3x², and p3 =…

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Q: 6. Can any of the given sets of 3-vectors below span the 3-space? Why or why not? (a) [1 2 1] [231]…

A: We have to check whether the given set of 3-vectors span the 3 space. (a) 1 2 1, 2 3 1, 3 4 2 (b) 8…

Q: 3.10. Rotate the vectors by 30%. *:[],三闾

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Q: (-8 1 4 (a) If A = 4 4 7 prove that A- = A' where A' is the transpose of A. 1 -8 4

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Q: 7. Find if the following expressions result in a scalar or vector quantity or they are meaningless.…

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Q: The set W={ 2х х —2х `); x E R} is Select one: O a. Closed under both vector addition and scalar…

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