Consider the set S = {2x² + 1, 2x – 4, 2x + x}. The set S spans P2. If t(a) — 6а? + 6х — 15 € Ра, 6x? + 6x – 15 e P2 , then t can be written as a linear combination of elements of S. That is, t(x) = — а - (2л + 1) +b . (2ӕ — 4) + с : (- 2»? + а). Determine a, b, and c a = 6 = C =

Q: f = {(-9, – 2), (-8, 5), (-6, 1), (- 3, 7), (–1, – 2),(0, – 10)} and g = {(-7,7), (-6, 6), (-5, 5),…

A: Given that, f = {(-9, -2), (-8, 5), (-6, 1), (-3, 7), (-1, -2), (0, -10)} g = {(-7, 7), (-6, 6),…

Q: f z-3x2- 4хy3 +6х,find. дудх

A: Given z=3x2-4xy3+6x we have to find ∂2z∂y∂x

Q: 15. Prove: If a, b, c, a, and M are constants and M = 0 then ax²y" + bxy' + cy has a particular…

A: Let us solve above problems.

Q: Show that A×(BxC) + Bx(CxA) + Cx(AxB) =0.

A: We have to prove that LHS=RHS

Q: Ifv = [ -2, 4], compute and draw 2v, 1/2 v, and -2v.

A:

Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: Let u = 4u + 5v (9, -2, -8) and v = (4, −3, −1).

A: The required solution is:<56,-23,-37>Explanation:

Q: Given m = 2xe2y and n = x³e-2y. Find if J=-16x³. ax am e2y e-2y 2x2 8 3e-2y e2y 16x 8x3

A:

Q: the constants c1 and c2 such that: (3;5)=c1(1;-2)+c2(2;-3)

A: Given (3;5)=c1(1;-2)+c2(2;-3)

Q: Let a = 5j + k and b - 27 + 3 + 2k. Find - 3ā – 36.

A: We can find the given vectors.

Q: Let A=(¹). 3¹). Find 3A³2A² + 5A - 12.

A: Given: A=1-123 We are required to find: 3A3-2A2+5A-I2

Q: Find the values of c1, c2, and c3 so that c1 (4, –6, 2) + c2(-4, 3, 0) + c3 (-2,0, 0) = (-4, –3,…

A:

Q: Vx+4 -2 1 limx¬0 ||

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Find a pair of integers x and y such that 66x + 48y = gcd(66, 48)

A:

Q: = 3x=6, g(x)=x-12, and h(x)=-2x-5 find each of the follow"

A:

Q: A manufacturer of hot tubs makes two kinds of hot tubs - Bill and Jane. Bill requires 8 hours of…

A: Given that bill hot tub requires 8 hours of labor and Jane hot tub requires 12 hours of labor.Also…

Q: Given w= (-4, 12), s=(-6, -2), and r=(4, 11), %3D find 6r-(w+s). 6r-(w+s) =(| , O)

A: This is related to vector addition sub, and mul

Q: ×: Attend a 4-year college Px: 0.1 X: Attend a junior college Px: 0.2 X: Attend a technical…

A: 1) The probability distribution is given as follows: Event Probability Attend a 4-year…

Q: (7, -8) and w=(-4,8), Given v= find v+w. v+w=

A: We know that, A vector in form of V→=a,b is represented as V→=ai^+bj^

Q: 1) Divide: 12x* – 7x3 + 7x² + x – 1 by 4x2 –- x + 2

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Q9. (0,3) – 2i +1 = а. - 2i + 2 b. -2 – 2i с. (-1,1) d. (1,–1)

A: Substraction of two complex numbers

Q: (Vx +10xdx

A:

Q: 4x, +2x, + x3 = -1 -4x, — 6х, + х, +Зх, %3 3 8x, +16х, — 3x, — 4х, %3D-2 20x, +10x, + 4x, – 3x, = 4…

A:

Q: If Q(x) = 7x³ + x and R(x) = 6x – 7x², find the following: %3D a) (Q – R)(x) =|| %3D b) (Q * R)(x)…

A: Given: Qx=7x3+x, Rx=6x-7x2 For finding Q-Rx,we substract Rx from Qx

Q: Find

A:

Q: Let P (x) = 2x - 15a + az?+ bx + c, where a, %3D Given that (x - 5) is a factor of P (r), find a…

A: It is given that,  P(x) = 2x4 - 15x3 + ax2 + bx + c It is given that, (x - 5) is a factor of P(x).

Q: (2, –1, 3) and b (-3, 3, 4). Calculate 2a – 3b and |a – b|. Clearly separate the Let a calculations.

A:

Q: If (x + 1, y – 2) = (3,1), find the values of x and y.

A:

Q: If A = 3j + 2k, B = 2i – 2j – 2k then Ax B

A: Use cross product of vector

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.