In each part, find a basis for the given subspace of R3, and state its dimension. a) The plane 2x − y + z = 0.b) The plane y + z = 0.c) The line x = 3t, y = −t, z = t.d) All vectors of the form (a, b, c), where a = b + c.

Q: Given P(A^c-complement)=0.40, P(B) =0.40, P(AUB)=0.75, P(A)= 0.60, P(B^c)=0.75 Find P((AnB)^c)

A: Additional Law of Probability gives P( A ∪ B ) =P(A) + P(B) - P(A∩B)

Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and…

A: We need to find the equation of line perpendicular to r→=(4, 1)+s(-3, 2),  s∈ℝ and passing through…

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

A:

Q: d) Check whether the given points P(2, -3, 4), Q(-1, 2, 3), R(0, 7, 1) are collinear or not. e) Find…

A:

Q: Q2) Find the coordinate vector [x]B of x relative to the basis B={b1, b2}:

A: Let us consider a vector V  with the basis b1,b2,......bn then any vector v∈V is written as linear…

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 the value of a so that the vectors a = (11, −29, 13), b = (46, 5, 37), and c = (a, -194,-70)…

A:

Q: Find a vector function that represents the plane that passes through thepoint p0 with position…

A: The plane passes through the point p0 whose position vector is r0→. The plane also passes through…

Q: Show that there are no integers a, b such that a² + 2ab+26² = 100000000003. Hint. Use mod 4…

A:

Q: Find the equation of the plane P spanned by vectors  v = (2,1, 3)  and w = (1,2,-1)  containing the…

A: The given problem is to find the equation of plane P that is spanned by given two vectors and…

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.