x+ y +z = 4 2х- Зу+2-2 -x + 2y - z = -1

Q: Prove the identity without evaluating the determinant (Using properties). a1 b1+ tai ci+rb1 + sa1|…

A: Use the below properties of the determinant. 1) The determinant remains unaltered if its rows are…

Q: Find the area óf the triangle with vertices (2,0), (4, 5), (7, 3) using determinants.

A: The area of a triangle by using the determinant method is shown below.

Q: Q.1. Use Cramer's rule to find x, in the linear system. 2x, +x, +x3 = 4, -x, +2x, = 2, 3x, +x, +3x,…

A: Solve it by using Cramer's rule.

Q: Prove the identity without evaluating the determinant (Using properties). a1 b1 + tai ci+rb1+ sa1 a2…

A: Some properties to be used are. (1) Adding or subtracting a multiple of a row(column) to another row…

Q: Use Cramer's Rule to solve the system. 15 56 -5 56 x - Gy 13 z = - (х, у, 2) %3D

A: The given system of equations: 56x-24y+21z=-45-112x+48y+63z=-157x-6y+7z=-13

Q: x + 4 y + 3z = 2, 2x - 6 y + 6z = -3, 5x - 2 y + 3z = -5 %3D (a) By using Cramer's rule (b) Verify…

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Q: Use Cramer’s rule, whenever applicable, to solve the system.

A: Given: 4x-y+3z=6 -8x+3y-5z=-6 5x-4y=-9 To find the values of  x,y and z by grammer's rule

Q: (4) Use determinant to find the area of the triangle with vertices (0, 0), (x1,Yı), and (x2, Y2) in…

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Q: Evaluate the determinants to verify the equation.

A:

Q: Use Jacobian determinants to test the existence of functional dependence between the paired…

A: Given,   Functions are-y1(x1,x2)=3x12+2x22y2(x1,x2)=5x1+1

Q: Compute the determinants using cofactor expansion along the first row and along the first column.

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Q: Evaluate the determinants to verify the equation.

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Q: Compute the determinants using cofactor expansion along the first row and along the first column.

A: Co factors of first row: Therefore determinant value is,

Q: Compute the determinants using cofactor expansion along the first row and along the first column.

A:

Q: 2. Use determinants to calculate the area of the triangle with vertices (-1,2), (5,-3), and (4,4).

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Q: Find the determinant. W(x5, x²) = fot 2x = (x²)(5x4)-(2x)(x5) The Wronskian ---Select--- equal to 0…

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Q: The velocity of a car, accelerating at uniform acceleration a between two points, is given by v = u…

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Q: Prove the identity without evaluating the determinant (Using properties). a1 bi + tai ci+rb1 + sa1…

A: We have to prove the identity…

Q: 1. If two Hermitian operators A and B commute, show that they can be simultaneously diagonalized.

A: Given :-  If two Hermitian operators A and B commute , then they can be simultaneously diagonalized.

Q: Use expansion by cofactors to find the determinant of the matrix.

A: Given,         wxyz21-152427-2410-3218-224035-32

Q: Prove the identity without evaluating the determinant (Using properties). a1 b1+ tai c1 + rb1 + sa1…

A: Let,  A=a1a2a3b1b2b3c1c2c3 Now, det A=a1a2a3b1b2b3c1c2c3         ~a1b1c1a2b2c2a3b3c3  (because the…

Q: Evaluate the determinants to verify the equation.

A:

Q: Compute the determinants using cofactor expansion along the first row and along the first column.

A: Now co factors of first row are

Q: Use of Cramer's Rule 2x, – 3x, = 5 X +x, = 5 [1 1][x, X

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Q: Compute the determinant by cofactor expansion. At each step, choose a row or column that involves…

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Q: 5 0 -7 2 - 6 0 0 2 8 4 -7 3 - 8 6 0 4 - 4 0 0 - 1 4

A: The Determinant is, (- 384)   The detailed solution is as follows below::

Q: Explain the operational determinant?

A: The operational determinant :- Consider a system of two linear differential equation  L1x+L2y=f1t…

Q: Prove the identity without evaluating the determinant (Using properties). a1 b1 + tai c1+rb1 + sa1…

A: Consider the LHS=a1b1+ta1c1+rb1+sa1a2b2+ta2c2+rb2+sa2a3b3+ta3c3+rb3+sa3. Use the sum property of…

Q: Give three examples of application of determinant in engineering

A: (1) Determinant can be used to find solutions of the multi variable linear equations.

Q: 3 1 1 4 1 4 1 V2 3 7 ら=|0 8. V. 2 8. 9 3 8 8. 3/4

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Q: Use the arrow technique to evaluate the determina 4 0 det 4 19 -5 -1 3

A: Given that: A=4004-1319-5

Q: 7. Use CRAMER'S RULE to solve the system: 2x-y-z=2 4x+y-z=-5 6x-2y +2z=17

A:

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

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Q: Compute the determinant by cofactor expansion. At each step, choose a row or column that involves…

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Q: -2 3 11 4 5 -3 4 -2

A: We need to find the Determinant.  Now, consider:…

Q: Use 2 methods in evaluating the determinant. 9 -6 -5| 1.) -1 7 2 4 6m8

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Q: Expand the determinant 2 3 4 A = 1 5 3 by Rule of Sarrus. 3 0 5

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Q: Let B={V₁ =,2 =, V3 =}. Use determinant to determine whether B is linearly independent or linearly…

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Q: Calculate the determinant using two different ways. 0 0 1 0 0–-1 0 0 -1 2 2 1 -1 2 1

A: In this question we have to find the Determinant.

Q: Compute the determinants using cofactor expansion along the first row and along the first column.

A: Let A=123231312 First we will find determinant using cofactor expansion along first row.…

Q: 1. Encuentre la ecuación del plano determinado por los puntos P(1,2,3) Q(2,3,1) R(0,-2,-1) 2.…

A: Vector equation of the plane passing through the three points with position vectors a, b and c is…

Q: Solve for the value of x, y and z using Cramer's Rule. e-3xe7 e5ye7z 3y 5z) + 3 = 10 e3ye3z (13 (5y…

A: First simplify all three equation in linear form . Simplify the equation e3xe5e3ye3z=e-3xe7e5ye7z .…

Q: Use a determinant to find an equation of the plane passing through the points.(0, 0, 0), (1, 0, 3),…

A: Consider the following points: 0,0,0, 1,0,3, 0,3,4 x1=0,y1=0,z1=0x2=1,y2=0,z2=3x3=0,y3=3,z3=4

Q: Expand the determinant of B by the second column and evaluate the occuring algebraic subdeterminants…

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Q: Let T: R² → R² be the linear operator given by 7 ] - ([ ; ) = [ - {|- } {} } -x + 2y Зх + у and let…

A: We can solve this using given information

Q: Use Cramer’s Rule to solve the system.

A: Rewrite the system of equations as 3x-7y=12x-3y=-1. Now in form of the matrix 3-72-3xy=1-1

Q: solve the system using Cramer's rule

A: Given,

Q: 4. Use Cramer's Rule to solve the system 2x1+6x2+ 8x3 4x1+15x2 + 19x3 2x1 + 3x3 16 38

A: We have to find the solution by cramer rule

Q: 2. For the set of equations 2x, + 5x, = 1 2x, + x, + x, = 1 3x, + x, = 2 (a) Compute the…

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