3. (a) Explain why there is no vector i such that (3, –1, 4) × J = (-5,1, –4). (b) Explain why there are infinitely many vectors i such that (3, –1, 4) × i = (-5, 1,4), then find all such vectors by expressing the components of all such vectors i in terms of a single variable.

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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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: The projection of the vector 5î + 5ĵ – 5k onto the vector –4î + 2ĵ – 4k. | |

A: We have to find out

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

A:

Q: let u = 2i -5j  ;   v =-3i+7j  ;    w=-i-6j Find each specified vector of scalar A. 3w+2v b.…

A:

Q: Show that vectors (86, 87, –46), (-8, –6, –2), and (-6, –7, 6) are linearly dependent-that is, there…

A: If vectors are linearly dependent then they can be expressed as a linear combination of each other

Q: { (1, 2, 1), (2, 1, 5) , (1, –4, 7) } (i) Prove that is linear dependent subset of R³. (ii)…

A: A set is linearly dependent if and only if one vector is linear combination of other vectors.

Q: Find a vector orthogonal to both = 10 2 and w = 2

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Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

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Q: (i) Prove that { (1, 2, 1) , (2, 1, 5) , (1, –4, 7) } is linear dependent subset of R³. (ii)…

A:

Q: The following question is from linear algebra : Factors the vector (6, -5, -1)t into three…

A: Given a vector  which s to be broken into three components .The component  depends on ,…

Q: Are the vectors = [−5_3 −1], v = [02-1] and w = [-25 21 -8] linearly independent? Choose If they are…

A:

Q: a) Find all the real numbers à such the vectors 1- x 1+x and x+1 1 are orthogonal.

A: Two vectors are said to be orthogonal if their dot product is zero. Dot Product There are two…

Q: Let Q "Ax – x'b – C be such that A is positive definite. | Which of the following statements is…

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Q: O Find a vector perpendicular to both i- 3j+2k and 5i-j-4k

A:

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.