1.4 Find a basis B3 for im(A') and a basis Bą for null(A*). Note that in the same vein as 1.2 and 1.3, these two subspaces are geometrically a plane and a line, respectively. (You don't have to show this, but you could find their equations to check for yourself.) 1.5 Show that the vector in B4 is orthogonal to the vectors in B1, and that the vector in B2 is orthogonal to the vectors in B3. 1.6 Show that B1 U B4 and B2U B3 are both' bases for R³.

Q: 1 Let C = [c1, c2, c3] = -1 2 3 -1

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Q: Let S be the subspace of R¹ consisting of the solutions to the following system of equations:…

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Q: B = (1, x+1, x² + x) forms an ordered basis for P3. Give the B-coordinate vector of each of the…

A: The coordinate vector of v with respect to  is given by such that .(a) Given .Comparing the…

Q: c. Find the coordinate vector of the polynomial q(t)=3t² − 6t+2, relative to the basis for P₂ in…

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Q: 2. Find a vector orthogonal to the nullspace of the matrix [1 27 6. 4 L5 -1 2.

A: According to the given information it is required to find a vector orthogonal to the null space of a…

Q: 6. Determine if the vectors vị = (1, -1,3, –1), v2 = (1, –1, 4, 2), v3 = (1, -1,5, 7) dependent or…

A: We have to find that given vectors are linearly dependent  or linearly independent.

Q: Find a basis for the indicated subspace of R³. The line of intersection of the planes with equations…

A: Let V be a vector space over a field F. A set S of vectors in V is said to be a basis of V if  (i) S…

Q: Find a vector orthogonal to both 7 -10 and w -10 -10 -4 7

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Q: ...... 4 -2 9. 8. The value(s) of h which makes the vectors linearly dependent is(are) - 88 because…

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Q: The vector x is in a subspace H with a basis B = {b₁,b₂). Find the B-coordinate vector of x. 2 b₁ =…

A: We are given that           b1 = (2, -3)t          b2 = (-1, 5)t        Now, x is in H with the…

Q: 5.- Demonstrate whether the vectors of the following vector space are linearly dependent or linearly…

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Q: s) Determine if these vectors for a basis for R³: linear combination of these vectors. 0·0-0--0- and…

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Q: Find the dimension of the subspace spanned by the given vectors: u₁ = (1, 3, -2,5), u₂ = (0, 1,-1,…

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Q: 2.6. Find the distance from a vector (1, 2, 3, 4) to the subspace spanned by the vectors v₁ = (1,-1,…

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Q: Find a basis of the subspace of R4 that consists of all vectors perpendicular to both Basis: 0 3 8…

A: Two vectors are perpendicular if their product is 0.

Q: For Problems 17–18, find a basis for the subspace W of the vector space V. Clearly indicate and…

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Q: In P,, find the change-of-coordinates matrix from the basis B= (1-2t+P,3-5t+41,1 B-coordinate vector…

A: Given B=1-2t+t2, 3-5t+4t2, 1+4t2. To find P2 that transforms B to C, where C=1,t,t2 PC←B=131-2-50144…

Q: x, consisting of a single vector with integer coordinates, whose entries are as small as possible.…

A: Given: a) The line passing through the origin in ℝ2 with equation y = 57x. b) The line passing…

Q: Let B = (1, x, x², x³) be an ordered basis for P3. Find the coordinate vector 8x³ + 2x²7x - 9…

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Q: Find the vector x determined by the given coordinate vector [x]g and the given basis B. 8-{8}-(-6) B…

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Q: 5. Suppose that a company records the following quarterly revenue (in millions of dollars) over one…

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Q: 5 Suppose that u = 1 2 and v= 0 are vectors in R³. Determine the smallest 2 --- 2 subspace H of R³…

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Q: 1. Write the vector 1 16 as a linear combination of the vectors 1 2 and 2 1

A: Let the given vectors be:w=-7116, u=-112, v=21-5. To Do: We have to write the vector w=-7116 as a…

Q: 1 3 1 2 A=2 6 4 002 4 I= I Y Z ພ () and 6 = 3

A: Solution to the system

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.