Write the vector 3 (if it is possible) as a linear combination of the vectors d1, d 2.

Q: Consider the following vectors: 17 -2 -2 u = | 2|, v w = and b 3 2 When b is expressed as a linear…

A: Here we solve the system of linear equation .

Q: -5 and 4 4 k are orthogonal. k =

A: We know that if two vectors u & v are orthogonal to each other then the dot product or scalar of…

Q: Find the sum of the given vectors. а - (4, 0, 1), ь - (0, 5, 0) a + b Illustrate geometrically. a +b…

A: Given  The vectors  are  a =(4 ,0 ,1)  and  b= ( 0 , 5 , 0)

Q: Let -2 V2 = iz = w = If possible, express w as a linear combination of the vectors v1, v2 and v3.…

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Q: Which of the following pairs of vectors are linearly independent? u = (1,0) and w = (0,2). u = (1,2)…

A: Given: Some pairs of vectors. To find: Which of the pairs are linearly independent. Linearly…

Q: 5. u = Write the linear combination of standard vectors i and j.

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Q: Choose the linearly dependent vectors in R Select one: a. O b. C. d. 1 2. 3.

A: Topic- vectors & matrix

Q: Find the component form of the resultant vector. 1) u =(-11, 2) b=(10,-4) Find: -u - b

A: As per guidelines, we'll solve only one question if multiple questions are asked. If you need any…

Q: Which of the following pairs of vectors are linearly independent? u= (1,2) and w = (-2,-4). u= (1,0)…

A: If an ordered pair (x,y) can be written as k(x,y) for k any integer.

Q: Determine if the vector v is a linear combination of the remaining vectors.

A: Given vectors are: v=123; u1=110; u2=011 If the vector v is a linear combination of the remaining…

Q: Choose the linearly dependent vectors in R Select one: a. b. С. 2. d.

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Q: write the given vector in terms of i and j. u= (-8,5).

A: It is given that, the vector u is, (–8, 5).Assume that, the symbol i represents the horizontal…

Q: Give an example of three linearly dependent vectors in R3 such that none of the three is a multiple…

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Q: Find the vector z, given that u- (9, 2, 7), 2,-1), andw = 0,-4

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Q: (d) Let w =(-39,22), v’i=(2–5), v°2=(5,-4), v°3=(-4,-1). If possible, express w as a linear…

A: In this question we need to multiply vectors by constant and have to find values of constant

Q: Find the value of k for which the vectors -4] -5 and -5 k are orthogonal. k =

A: Let the two vectors be- a →=-20-51        and  b→= -4-50k It is given that both the vectors are…

Q: Which of the following sets of vectors in R² is linearly dependent? A. {(1,0), (0, 1)} B. {(1,0),…

A: A set of vectors is said to be linearly independent if the matrix with these vectors as columns has…

Q: Find the value of k for which the vectors 2 1 2 and -3 5 k are orthogonal. k =

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Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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Q: Consider the vectors V1, V2, V3 and b. 1 2 8 -2 V1 ,V3 -13 6. 12 18 Write b as a linear combination…

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Q: Determine whether the vectors v1=[1 2 1]^T , v2=[10 2]^T and v3=[5 6 7]^T are

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Q: Write each vector as a linear combination of the vectors in S. S = {(2, -1, 3), (5, 0, 4)} (a) z =…

A: We can evaluate this problem as follows:

Q: Find three nonzero vectors a, b, and c such that a × b = a × c = 0but b = c.

A: Find nonzero vectors a, b ,c such that a×b=a×c=0 but b≠c. If two vectors are parallel then their…

Q: Write each vector as a linear combination of the vectors in S. S = {(2, -1, 3), (5, 0, 4)} (a) z =…

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Q: Find the length of the vector. v= (4, 3) M -| 43

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Q: Choose the linearly dependent vectors in R. Select one: a. O b. C. d. 1 -1 -2

A: Suppose u and v be 2x1 vectors then u and v are linearly independent if det(u,v)≠0. If det(u,v)=0…

Q: Determine if the vector 2 b = 3 5 can be written as a linear combination of the vectors V₁ = 1 and…

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Q: Determine whether the vectors are linearly independent or linearly dependent. 7 9. [5] v, = |0|v, =|…

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Q: Determine whether the vector v is a linear combination of the remaining vectors. v = 3

A: (1).  The given vectors are: v→=12 ,  u1→=-1   3    and    u2→=   2-3

Q: Choose the linearly dependent vectors in R'. Select one: а. O b. O d. -2

A: The solution is given below

Q: га- Find an equation that describes all values of a, b, and c for which the vector w = |b| is NOT a…

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Q: Consider the vectors V1, V2, V3, and b. V1 4 V2 = 5, V3 6 ,b = 7

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Q: Find a vector perpendicular to the graph of z = - 3 x2 + 9 y2 – 7 x y at the point (8, 2, -268).

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Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

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Q: Consider the vectors x"(t) = (10) and x"() - 8t

A: Given, The two vectors  and

Q: (a) Suppose that a and b are two unit vectors in R^3, and a·b=11/24. Find the norm of the vector 4a+…

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Q: Which of the following vectors are not linearly independent? 日L O B O A

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Q: Let 52D If possible, express w as a linear combination of the vectors 71, 02 and 3. Otherwise, enter…

A: We have to write w as a linear combination of v1 , v2 and v3.

Q: Determine whether the following vectors are linearly independent in R3:

A: Given vectors, Let us set up a homogeneous system of equations, The set S = { X, Y, Z } of vectors…

Q: Show that the following vectors are linearly dependent, and then write one of the vectors as linear…

A: Concept: The vectors are linearly independent only when The determinant of the vectors are equal to…

Q: Consider the following vectors: 2 -2 and b -3 u , V 4 When b is expressed as a linear combination…

A:

Q: Express the resultant vector as a linear combination. f=-3i - 10j %3D g = 11i + 5j Find:-6f +2g

A: To find -6f+2g.

Q: Let S = { t² + 1, t² – 1, t – 2}. - 2. If S is linearly independent in P2, write 2t2 – t + 5 as a…

A: Three vectors A,B,C are said to be linear dependent, then there exist three numbers a,b,c such that…

Q: a a

A: For first figure. a→+a→+b→+d→-c→=02a→=-b→-d→+c→a→=-b→-d→+c→2    Answer

Q: Consider the following vectors: -3 4 4 4 1 , v = 1 , w = 2 |, and b = -4 u = 3 3 When b is expressed…

A:

Q: Determine if the vectors t= %3D(-16, 24) and s= (3, 2). are orthogonal, parallel, or neither.

A: We have to calculate dot product and magnitude of the given vectors

Q: Express each column vector of AA as a linear combination of the ordered column vectors c1, c2, and…

A: Express each column vector of AA as linear combination of the order column vectors c1, c2 and c3 of…

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.