1. Let T be the set of all real 2x2 matrices with zero trace: T = {A € M2(IR) : tr(A) = 0} (a) Prove that T is a subspace of V = M2(R). (b) Construct a basis for T. Prove that your collection does in fact form a basis (Hint: You need to decide what a typical element of T looks like. What has to be true about the entries along the main diagonal of A for tr(A) = 0?) [1 -2 0 5 1 1 0 2. Let A = (a) Find a basis for the nullspace N(A) of A (indicate two sets in your answer: the set which forms your basis and the set which forms your nullspace). (b) Find a basis for the column space Col(A) of A (give two answers again as in (a): write down the basis for Col(A) and write down Col(A) itself).

Q: One of the following subsets of R² is not subspace. Select one: а. X1 S={ X1=2x2} b. S={ ,X1 =X2} C.…

A: We will check that which subset is not a subspace of R2

Q: Show algebraically that the perspective matrix preserves order of z values within the view volume.

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Q: Use Axioms only to prove that the the solution to the equation 2x + y + 3z = 0 is a subspace of R³.

A: The given equation .To prove that the solution to the equation is a subspace of .

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Q: Please define the four fundamental subspaces? Please have your answer types.

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Q: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?

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Q: Are zero matrices also called diagonal matrices 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

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Q: 3. This problem is about set addition and subspaces. Let di and d2 = span{di}, %3D 1 U = span{d2}.…

A: Sum of two subspace

Q: but not こ *6A-エ none of thesce

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Q: Draw Figure 4.2 to show each subspace correctly for A = and B = 36 3

A: Given matrix is .Here A is a linear map from  to  . So, we get n=m=2.Find the row space of A:Find…

Q: Is it possible to solve it using words like claim as my professor did in his example in other photo?…

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Q: Sketch all four subspaces associated to mat 1 2 A = 3 6

A: Respected student, By Bartleby guidelines we have solved all the four subspaces with the first…

Q: Section B: Determine of the following set W is subspace of V=R³: W-{(a, 1, 1): a ER).

A: We have to determine whether the set W is a subspace of V=R3.…

Q: АT (Ь — Ах) — ӧ. Interpret this statement in terms of the fundamental subspaces of A.

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Q: True or False, S is a subspace of R 3 x1 (8] x2 x3 S = O True O False 2x1 + x3 = 0, x1 + x2 = x3 = 0…

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Q: Part 1: Find the inverse of the matrix A, if it exists. A 033 -4 03 o] 060 06

A: The matrix is: A=033-403060 To Do: We have to find the inverse of the matrix if it exists.   Note-…

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Q: How do you find a basis for a given subspace? May you please throw in an example too?

A: See the attachment.

Q: True or False? Suppose A is an 7 x n matrix. If there is an 7 x n matrix D such that AD = I, then…

A: True. This is a property of invertible matrices, which are square matrices that have an inverse. If…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.