The set of all 2X2 matrices with ones on it's main diagonal is a subspace of R2x2 . true or false

Q: If the system Ax = b is inconsistent, then b must have a component in which fundamental subspace of…

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Q: Is the union of two subspaces of a vector space, a subspace.

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Q: The set of all polynomials of the form ax³ bx² cx + 2, where a,b and can real numbers is a subspace…

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Q: Determine whether the subspaces are orthogonal.

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Q: What is the dimension of the subspace or the space of 5 x 5 matrices (ai) sucn that a11 +...+ az5 =…

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Q: , find the orthogonal projection matrix on the subspace defined by the equation: 2х-у-3z-0.

A: a) Let v1 = [3,6,0] and v2 = [0,3,-1] be two vectors on the plane As we have 2(3)-6+3(0) = 6-6+0 =0…

Q: Is the set of all 2 x 2 matrices of the form a 1/ 1 b , where a and b may be any scalars, a vector…

A: The given set is a11b | a, b∈K. It is known that any subspace should contain the identity element.

Q: Determine whether the subspaces are orthogonal.

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Q: Give an example of a subset (not subspace) of R3 that has an infinite number of elements, is closed…

A: A subset W of vector space V over the scalar field K is a subspace of V if and only if following…

Q: Why are [0,1] and (0,1] which are subspaces of the real number system with the usual topology not…

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Q: What is a linear subspace?

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Q: Find a basis of the subspace ofRª defined by the equation 7x1+9x2+ 6x3 + 5x4 = 0. Basis:

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Q: The set of all nxn matrices whose entries are negative or zero is a subspace of Mnn: True False

A: The answer is true

Q: Determine whether the following are subspaces of R2×2: The set of all 2 × 2 lower triangular…

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Q: Find a basis for the subspace of Mnxn consisting of all diagonal matrices.

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Q: The set of all 3 x 3 matrices of the form 0 0 0 0 0 -5x 0 0 0 where x is a real number, is a…

A: Given :M=00000000-5x

Q: Let L be the subspace of V that contains all the real n x n lower triangular matrices. What is the…

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Q: Suppose that A is an n x m matrix of rank 5, the nullity of A is 4, and the image of A is a subspace…

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Q: Find a basis for the subspace of R* spanned by S. S = {(-20, –7, 2, –4), (21, 7, –2, 4), (-9, –3, 1,…

A: We have given set of vectors ,  S = -20 , -7 , 2 , -4 , 21 , 7 , -2 , 4 , -9 , -3 , 1 , -2 , -18 ,…

Q: What can be said about Nul A if A is a 5×7 ​matrix? Could it be the zero​ subspace? Why or why​ not?

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Q: In R4 , find the dimension of the subspace spanned by the vectors {(1, 1, 1, 1)T , (1, 2, 2, 2)T ,…

A: Given vectors are {(1, 1, 1, 1)T , (1, 2, 2, 2)T , (1, 1, 2, 1)T , (2, 2, 3, 2)T , (4, 5, 6, 5)T }.

Q: If V is direct sum of two subspaces, then every vector in V has .representation

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Q: Find the dimension of the subspace spanned by the given vectors.

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Q: Find a basis for the subspace of R4 spanned by S. S = {(2, 9, -2, 53), (-5, 2, 5, –2), (8, –5, –8,…

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Q: Find a basis for the subspace of R4 spanned by S. S = {(-11, 6, 4, 8), (-6, 3, 2, 4), (-2, 1, 1, 2),…

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Q: Show that the solution vectors of a consistent non-homogeneous system of m equations in n unknowns…

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Q: Find a basis of the subspace of R defined by the equation -7x1 – 5x2 – 4x3 = 0.

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Q: Let A be a 80 x 90 matrix (80 rows and 90 columns). Does the homogeneous 0 always has nonzero…

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Q: Is W=set of upper triangular 3x3 matrices a subspace of V= all 3x3 matrices? Support your answer to…

A: According to the given information, it is required to show that set of all upper triangular matrices…

Q: The set of real matrices with 3 rows and 3 columns is the known matrix addition of M3 × 3 and Show…

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Q: The set of all nxn matrices A such that the linear system Ax = 0 has only trivial solutions are the…

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Q: The set of all 3 x 3 matrices of the form 1 0 0 1 Lo o 0 0 Select one: True O False + 13x3 where a…

A: Answer: The solution is as given below:

Q: Is W=set of upper triangular 3 x 3 matrices a subspace of V=all 3 x 3 matrices?

A: In this question we need to check W is a subspace. so we need to check two properties * w1 and w2…

Q: The set of all nxn matrices whose entries are odd integers is a subspace of Mnn. Is it true or…

A: A subset of a vector space is a subspace if it is a vector space itself. First of all the space…

Q: (a) If a 7 by 9 matrix has rank 5, what are the dimensions of the four subspaces? What is the sum of…

A: Use the given information.

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

A: See the attachment.

Q: Find a basis of the subspace of R* defined by the equation 2x1 + 9x2 + 4x3 + 9x4 = 0. %3D Basis:

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Q: The set of all 3 x 3 matrices of the form 1 0 0 0 1 0 00 -a Select one: True O False + 13x3 where a…

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Q: Is it true that the set of all 4 x 4 matrices with a trace of 0 is a subspace of Max4? If so, prove…

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Q: Give an example of a two-dimensional subspace of R4 .

A: Consider two-dimensional subspace of R4 is, u1=1111, u2=110-2

Q: Find the dimension of the subspace Hof R2 spanned by

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Q: Find a basis for the subspace of R4 spanned by S. S= {(5, 9, -5, 53), (-2, 5, 2, -5), (8, -2, -8,…

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Q: Show that (4, 14, 8) lies in the subspace of R generated by (-1, 3, 1) and (4, 1, 2). (4, 14, 8) =…

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Q: Find a basis of the subspace of R° defined by the equation 3x1 + 9x2 + 2x3 0. Basis:

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Q: Let A be a 3 × 2 matrix with rank 2. Give geometric descriptions of R(A) and N(AT ), and describe…

A: Given: Rank of matrix A3x2 is 2. Then the dimension of column matrix A dimR(A)=2 Also given that the…

Q: What is the dimension of the subspace 0 2 3 1 H = x1 x2 x3 X4 ER¹ : 2x1 3x2 + 4x3 5x4 = 0 ?

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Q: Find a basis of the subspace of R defined by the equation 3x1 – 7x2 + 6x3 0. Basis:

A: Evaluation of basis problem.....

Q: Why are [0,∞) and (0,∞) which are subspaces of the real number system with the usual topology not…

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Q: Determine whether the subspaces are orthogonal.

A: Given,  S1=span1,1,1,1S2=span-1,1,-1,1,0,2,-2,0

Q: is a subspace of M23-

A: A nonempty subset W is a subspace of a vector space V if, whenever w1, w2 are elements of W and α is…

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.