Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below. 1 3 1 -2 - 13 13 1 -2 - 13 2 7 4 -2 - 23 0 1 2 2 3 A = -3 - 12 - 9 45 0 0 0 13 11 -3 - 42 0 0 0 A basis for Col A is given by 9|} (Use a comma to separate vectors as needed.)

Q: give the matrix A = {(1, -2, -4, 3 , -2), (0 , 3, 9, -12 , 12), (0, 0, 0, 0,0) (0, 0, 0, 0, 0)} a.…

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Q: 0 3 -6 6 Consider the matrix A = 3 -7 8 -5 3 -9 12 -9 (a) Suppose Nul(A) is a subspace of R" and…

A: Let T be linear transformation from T: ℝn→ℝm then N(T) is subspace of ℝn and R(T) is subspace of ℝm…

Q: The vector a can be projected onto the subspace spanned by uj and 02. This resulting projection of ā…

A: We are given that a→=-1-1011, v1→=1825,  v2→=20-19-4 and vector  a→ is projected onto the subspace…

Q: write answer as fraction -(1/2)^3

A: We know , (a/b)n = an/bn

Q: 7.) Find a basis for the subspace V of R4 consisting of all vectors of the form (a, b, c, a +b+c),…

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Q: Find a basis for the subspace of R'consists of all vectors of the form (a, 2a + b, b, 0). State its…

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Q: 1 8 Find a basis for the subspace of R³ consisting of all vectors 2 such that 6x1 - 7x2 - 4x3 = 0. 3…

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Q: Find a basis for the subspace spanned by the given vectors. What is the dimension of the subspace? -…

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Q: find an orthogonal basis and then an othnormal basis for the subspace U of R3 spanned by v1 =…

A: The objective of this question is to find an orthogonal basis and then an orthonormal basis for the…

Q: What is the matrix P = (P; ;) for the projection of R³ onto the subspace V spanned by the vectors 1…

A: Given Data: Let us consider the given data, a1=122 , a2=2-32b=35-3 To Find: The value of P1, P2 and…

Q: Part I: Consider the subspace of M2x2 that has [23] 32 is the coordinate vector of Part II: What…

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Q: Find a basis for the subspace spanned by the given vectors. What is the dimension of the subspace? 1…

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Q: 4. Find a basis for the subspace spanned by the given vectors. What is the dimension of the…

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Q: Let H = span {(16, -21, -14), (-17, 20, 13), (-23, 28, 18)}. }. vector A basis for the subspace HC…

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Q: Consider Sspan 1 -3 5 3 -10 10 What is the dimension of S? -3 10 -10 which is a subspace of R³ Find…

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Q: Asap show correct work and answer

A: ∴any vector in the null space can be written by using the vector (1,-1,1).So, dimension of the null…

Q: t ₁, ₂ and 3 be the columns of A, let B = {a₁, a2, ã3} and let H = span(B). a. The number of vectors…

A: Given A is a 3*3 matrix and B is set of vectors containing columns of matrix A and H= span(B).

Q: Determine a basis for the subspace of R that consists of vectors the form (a, b, c, a - 5b + 4c).…

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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: P₁1 = P₂1 = P31 = P1 = P2 = What is the matrix P = (P; ;) for the projection of a vector b E R³ onto…

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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.