efine the binary operator  ∇∇  by:     a∇b=9a∇b=9  Find each of the following:  3∇5=3∇5=    8∇8=8∇8=   5∇3=5∇3=    v∇n=v∇n=

Q: Are the following two sets of coefficients orthogonal? -1, 0, 0, 1 -1, 1, 0, 0 Yes No

A: Given data is as follows: -1,0,0,1 -1,1,0,0 Yes the following sets of coefficients are orthogonal as…

Q: In a mass spring damper system, the acceleration, a m/s², velocity, v m/s and displacement, s m are…

A: cramer's rule to find solution of linear equation of 3 variable…

Q: a a. Evaluate: a a a b. Evaluate: 0 0 0 a a a al la a a a a a a c. Evaluate: 0 0 a a 0 0 0 a d.…

A:

Q: d The mapping is a linear operator. Is 2 a linear operator? Is c a linear operator? da de

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Q: 12101 4-1010 13131 01912 12101

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Q: Use the cofactor expansion to compute the following determinant: 5 6 5 det -3 9 7 %3D 6 9-8

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Q: H.W:- Used Cramer's Rule to find the value of the variables in the following equations: 5x + 4y = 11…

A: Creamers rule is used

Q: H.W:- Used Cramer's Rule to find the value of the variables in the following equations: A. 3x - 2y =…

A:

Q: Let x 4 || - N and y = Find the vector v = 3x - 4y and its additive inverse. 18 [2] 4

A: The additive inverse of a vector v = <a , b> is  - v = <-a , -b>

Q: Given a generic 2x2 matrix A, and a second 2x2 matrix C, show the following: d. Using property c…

A: In this question, concept of matrix operation is applied. Matrix  A matrix is a rectangular array…

Q: b) - a +b-c+d = 0 – 2a + b+c-3d = 0 a + 2b - 3c + d = 0 2a + 3b +4c- d 0

A: Let us considre the system of matrix Ax=b Using Cramer's rule, the solution of the system of…

Q: a 12 Let A 0 a 1 For what value of a is A diagonalizable? Explain your 00 a answer.

A:

Q: I need help with this assignment. they all should have 4 places after the decimal place unless the…

A: Solution:

Q: ={b₁,b2} and C= {C₁,C₂} be bases for a vector space V, and suppose b₁ 1 Let B= a. Find the…

A:

Q: Evaluate the following determinants by inspection:

A:

Q: Let A be a 7 x 7 matrix. Write down the number of different expressions for the determinant of A we…

A: The minor matrix is the determinant of the matrix that is formed by deleting the ith row and jth…

Q: Solve for the value of x, y, and z using Cramer's Rule 8x +15y + 3z = 143 3x - 7y + 13zi = -62 +…

A: We will find out the required solution using Cramer's rule.

Q: Verify that (AB)T = BTAT.

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Q: 2. 5. 2.6= 3 and c = 5. Let a = %3D 3 Compute (1) a + c (2) a + 6+ a (3) c+d +b

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Q: Match each vector field with its graph. xi + yj + zk (x² + y² +2²)3/2 C# 27= = 3.7 = x² + yj D#…

A: According to the given data, match each vector field with its graph.

Q: 2. If 8t²-t+4 is expressed as a linear combination of 3t²+t+1, 2t²-t+1 and 3t²-t+2; which of the…

A: Find scaler constant

Q: Consider the linear operator T: R? → R² defined by the following equations. w1 = 3x1 + 11x, W2 = X1…

A: we have to find the inverse of T          (i.eT-1(w1,w2))where T:R2→R2 is given by…

Q: 1+a² – & 2ab 2ab -26 - 1- a² + b = (1+a² +&)* 2a 26 -2a 1- a – 6

A:

Q: Suppose the operators Å and B are projection operators. Show that the sum of two projection…

A:

Q: Find the determinant of x from the given matrix: 4 -123 2021 10 301 14 2 4 5 -35 -30 -28 -25

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Q: Express the determant expression of a 3 X 3 matrix using cofactor and minor, Using this, try to…

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Q: Evaluate the following determinants by inspection:

A:

Q: Draw the arrow diagram for each composition of relations S and T represented by matrices: S: 101 T:…

A: From the matrix representation of matrix we get             123S=123 101011110Relation S ={ (1, 1),…

Q: Solve the problem. Let A = 1-3 2 -2 5-1 3-6-3 and b = ¹₂ --B b3 Determine if the equation Ax = b is…

A:

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.