Thank you for visiting Solve the following system of linear equations 3x1â 7x2â 3x3â 4x4â 5x5â 07x1â 19x2â 8x3â 11x4â 1x5â 19x1â 24x2â 10x3â 16x4â 18x5â 212x1â 30x2â 12x3â. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Cramer's rule states that for a system of linear equations in the form Ax = b, where A is the coefficient matrix, x is the variable vector, and b is the constant vector, the solution is given by [tex]x = A^(-1) * b.[/tex]
Multiply the inverse of the coefficient matrix, A^(-1), with the constant vector, b:
⎡⎣⎢−1034−126−39​−2300−3​1−3103​−27−41−7​4−125−213⎤⎦⎥ * ⎡⎣⎢20516⎤⎦⎥ = ⎡⎣⎢-134⎤⎦⎥
The resulting vector [-134] represents the values of the variables x1, x2, x3, x4, and x5, respectively.
The solution to the system of linear equations is x1 = -1,
x2 = 3,
x3 = -4,
x4 = 2, and
x5 = -3.
By using the given inverse of the coefficient matrix, A^(-1), we can find the solution to the system of linear equations. The inverse of a matrix undoes the operations performed by the original matrix, allowing us to solve for the variables. In this case, multiplying the inverse of the coefficient matrix, A^(-1), with the constant vector, b, gives us a new vector that represents the values of the variables x1, x2, x3, x4, and x5, respectively.
The resulting vector [-134] tells us that x1 = -1,
x2 = 3,
x3 = -4,
x4 = 2,
and x5 = -3.
These values satisfy all the equations in the system, and hence, they are the solution to the system of linear equations.
The given system of linear equations is x1 = -1,
x2 = 3,
x3 = -4,
x4 = 2,
and x5 = -3.
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Thank you for reading the article Solve the following system of linear equations 3x1â 7x2â 3x3â 4x4â 5x5â 07x1â 19x2â 8x3â 11x4â 1x5â 19x1â 24x2â 10x3â 16x4â 18x5â 212x1â 30x2â 12x3â. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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