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A=[4 1 3] [2 1 1 ] [3 1 -2]....this is a matrix ...we have to solve the equations..4x+2y+3z=1 x+y+z=1 3x+y-2z=2 and find A inverse
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A=[4 1 3] [2 1 1 ] [3 1 -2]....this is a matrix ...we have to...
**Solving the Equations**
To solve the system of equations using the given matrix A, we can rewrite the equations in matrix form as AX = B, where X = [x y z]^T and B = [1 1 2]^T.
The matrix equation AX = B can be written as:
[4 1 3] [x] [1]
[2 1 1 ] * [y] = [1]
[3 1 -2] [z] [2]
To find the values of x, y, and z, we need to find the inverse of matrix A and then multiply it with B. Let's now find the inverse of matrix A.
**Finding the Inverse of Matrix A**
To find the inverse of matrix A, we can use the formula:
A^(-1) = (1/det(A)) * adj(A)
where det(A) is the determinant of matrix A and adj(A) is the adjugate of matrix A.
To calculate the inverse of matrix A, we need to find its determinant and adjugate.
**Calculating the Determinant of Matrix A**
The determinant of a 3x3 matrix can be found using the following formula:
det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)
where a, b, c, d, e, f, g, h, i are the elements of matrix A.
Using the given values, we can calculate the determinant of matrix A:
det(A) = 4(1*(-2) - 1*(-1)) - 1(2*(-2) - 1*3) + 3(2*1 - 1*3)
= 4(-2 + 1) - 1(-4 - 3) + 3(2 - 3)
= 4(-1) - 1(-7) + 3(-1)
= -4 + 7 - 3
= 0
Since the determinant of matrix A is 0, the matrix is singular and does not have an inverse. Therefore, the system of equations given does not have a unique solution.
If you have any further questions, feel free to ask.
To solve the system of equations using the given matrix A, we can rewrite the equations in matrix form as AX = B, where X = [x y z]^T and B = [1 1 2]^T.
The matrix equation AX = B can be written as:
[4 1 3] [x] [1]
[2 1 1 ] * [y] = [1]
[3 1 -2] [z] [2]
To find the values of x, y, and z, we need to find the inverse of matrix A and then multiply it with B. Let's now find the inverse of matrix A.
**Finding the Inverse of Matrix A**
To find the inverse of matrix A, we can use the formula:
A^(-1) = (1/det(A)) * adj(A)
where det(A) is the determinant of matrix A and adj(A) is the adjugate of matrix A.
To calculate the inverse of matrix A, we need to find its determinant and adjugate.
**Calculating the Determinant of Matrix A**
The determinant of a 3x3 matrix can be found using the following formula:
det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)
where a, b, c, d, e, f, g, h, i are the elements of matrix A.
Using the given values, we can calculate the determinant of matrix A:
det(A) = 4(1*(-2) - 1*(-1)) - 1(2*(-2) - 1*3) + 3(2*1 - 1*3)
= 4(-2 + 1) - 1(-4 - 3) + 3(2 - 3)
= 4(-1) - 1(-7) + 3(-1)
= -4 + 7 - 3
= 0
Since the determinant of matrix A is 0, the matrix is singular and does not have an inverse. Therefore, the system of equations given does not have a unique solution.
If you have any further questions, feel free to ask.
Community Answer
A=[4 1 3] [2 1 1 ] [3 1 -2]....this is a matrix ...we have to...
[4 2 3] [x][1 1 1]=[[y][3 1 -2] [z]first show this step than apply the method of multiplication of matrix than u will get the same eq as given in the question n then solve it by linear eq.....answers which i got by solving them r:x=-1/2y=7/2z=7/4
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A=[4 1 3] [2 1 1 ] [3 1 -2]....this is a matrix ...we have to solve the equations..4x+2y+3z=1 x+y+z=1 3x+y-2z=2 and find A inverse
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A=[4 1 3] [2 1 1 ] [3 1 -2]....this is a matrix ...we have to solve the equations..4x+2y+3z=1 x+y+z=1 3x+y-2z=2 and find A inverse for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A=[4 1 3] [2 1 1 ] [3 1 -2]....this is a matrix ...we have to solve the equations..4x+2y+3z=1 x+y+z=1 3x+y-2z=2 and find A inverse covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A=[4 1 3] [2 1 1 ] [3 1 -2]....this is a matrix ...we have to solve the equations..4x+2y+3z=1 x+y+z=1 3x+y-2z=2 and find A inverse .
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