Let vectors 71, 72, 73, 74 are given by 72 = -a,+đ, + a+ 4, 1 3 ন = ते। - ते; + वे.. न, = 2े + 4ते; + 2ळे, 3 3 where d1, d2, d 3, a4 is a basis of a vector space V. The dimension of W span{1, 72, Y3, Y4} is equal to (choose the correct answer) o 1 o 2 o 4 o 0

Q: 3. Determine if the sets of vectors given are LI or LD and explain how you know. a) {(3,4),…

A: Here we apply theorems from linearalgebra.

Q: Find 3-dimensional vectors V₁, V₂, V, satisfying V₁V₁ = 4, ₁₂ = -2, V₁ V₂ = 6, V₂ V₂ = 2₁ V₂ V₂ =…

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Q: Given three non-zero vectors, a, b & C, is it possible to evaluate a b Explain with an example. •6•²

A: We have given three non-zero vector.

Q: Are the vectors (1, 2, 3, 4), (2, 3, 4, 5) and (3, 4, 5, 6) lin indep?

A:

Q: Assume that A is row equivalent to B. Find bases for Nul A and Col A. - 2 8 -2 - 8 10 8 11 A = 2 -…

A: The null space of any matrix A consists of all the vectors B such that AB = 0 and B is not zero

Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: A = [-2,4,-2,-4,        2,-6,-3,1,        -3,8,2,-3,        0,2,5,3]  Find a non-zero vector R^4…

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Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3),…

A: We can solve the given problem as follows:

Q: There are four vectors (1,2,3), (1,-1,2), (2,4,6) and (2,6,c). If there is a condition in which the…

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Q: Q4\ Find the vector if its magnitude equal √90 and its unit vector is 4i 5j 7k + √90 √90 √90 -

A:

Q: Construct a vector that is perpendicular to the plane containing (−2, 4, 1),(3, 3, -1) and (1, 0,…

A: Construct a vector that is perpendicular to the plane containing (-2,4,1),(3,3,-1) and (1,0,2)

Q: If the cross product of two nonzero vectors is the zero vector, then each of the two vectors is a…

A: Explanation of the answer is as follows

Q: Find a vector with initial point (-5, 0, -2) and terminal point (-4, -5,7). Then find a unit vector…

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Q: Check that the space generated by the vectors (1, 3, 5), (1, 4, 3), (1, 1, 9) is equal to the space…

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Q: Do the vectors ū = i+j-4k, V= -5i +3j-7k and w'= -i +4j+2k plane? 1ie in the Same

A: We have to check whether the vectors u→=i+2j-4k, v→=-5i+3j-7k, and w→=-i+4j+2k are in the same…

Q: ind {(1,-1,0,2), 3,4,2,1), (1,0,0, 1)} ench vecton th anther There three is this combinat ave

A: In this question we will use basic of calculus i.e concept of vector calculus. We will simply form…

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

A: we will write the given vector as linear combination of vectors in as and find the unknown…

Q: Find a unit vector in the direction of

A: Given that,   vector = <6, 3, 2> = u¯ (Say)   Unit vector = u¯u = <6,3,2>62+32+22 =…

Q: Vector A is 6 inches long and is 60° above the +x-axis in the first quadrant. While vector B is 6…

A: Shown here are two vectors as given in the question. Resolve the first and second vector on the x…

Q: 4) IF = (6,-8) m, B = (-8,3) m, AND A = (26, 19) m, FIND THE UNKNOWN CONSTANTS AND B SUCH THAT ab +…

A: As Per Bartleby Answering Guidelines We Solve  Only First One Problem Solution - 4  :  Given that…

Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A:

Q: Determine the following three vectors {, , } forms a basis for R^3. Expalain your answer.

A: Answer  Given  <2,1,0> , <4,2,2> and <-2,-1,3>  Let check whether they are…

Q: 0 a=27 +63 +-4k, Б=-32-97+62

A: Given Vectors are as follows Let the angle between a and b be denoted by

Q: 5 3 -2 -3 w = -3 |; A= 4 -5 2 2 -5 4 -1 . Determine if vector w is in Nul(A)

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Q: 4 16 -- 12 -21 4. Is the vector in the span of the vectors 10 12 -8 and 8 ? Explain!

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Q: Express the vector b = a₁ + a2 + 2 -4 as a linear combination of the vectors a₁ = a3 = b -2 3 7 , a₂…

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Q: Suppose that u₁ and u2 are vectors with ||u₁|| = 2 and ||u2|| = 3. You are also given that u₁ · U₂ =…

A: Given that  and  are vectors such that .Given that  and  for .We need to find  for .We need to…

Q: If vector u=2:1+2:/ and vector V =5./+4/, simplify each of the following, writing your final answer…

A: Given:    u = 2i + 2j    v = 5i + 4j

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.