11. Find a basis for the set of vectors in R³ in the plane x + 2y + z = 0. [Hint: Think of the equation as a “system" of homogeneous equations.]

Q: 4. State with a brief explanation whether the following statements are true or false. (a) The…

A: a) true The vectors (1 ,0) and (0,1) is linearly independent. We know that linearly independent set…

Q: 4 В T(t+h) A 21 y 01 2

A:

Q: -54 ) Express the vector i and y -5 as a linear combination of a = 4 y.

A:

Q: 11. Let / be the intersection of the two planes 2x - 3y + 4z = 2 and x-z = 1 a. Find a vector…

A: Let l be the intersection of the following two planes(a) To find a vector equation of l.(b) To find…

Q: Find a basis for the set of vectors in R³ in the plane x - 3y + 6z = 0. [Hint: Think of the equation…

A:

Q: Find a basis for the set of vectors in R³ in the plane x-6y + 5z = 0. [Hint: Think of the equation…

A:

Q: 1. Determine whether the points A(3,4,-1) and B(1,-1,0) lie on the line with vector equation…

A: Given vector equation :

Q: 8.) Find a vectorx such that 5x-2v=2(u-5x) SOLUTION

A:

Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: . The distance of a point in the 3-D system from the origin a. is defined by the absolute value of…

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

A: The given vectors are  a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k

Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: 2. Given the two vector combinations a+ 4b = 4i + 4j + 6k, a- 2b =i+7j + 3k, find a and b.

A:

Q: 5. Show that the vectors a = 3i-j+ 4k, b =i-3j–2k and e = 4i– 3j+2k are linearly independent. Find…

A:

Q: Determine all three dimensional vectors that are orthogonal to v = 5î – 51 – 5k

A:

Q: Find the vector and the cartesian equations of the plane containing the point î+ 2j – k and parallel…

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.