Question

Solve the system of linear equations by matrix Inversion method, 3x+5y = 1 and 2x+y=3.​

Answer 1

Answer: The solution for the system of linear equations 3x+5y = 1 and 2x+y=3 is x = 1 and y = -1.

The system of linear equations can be represented in matrix form as

                       AX = B,

Where:

                       A = [[3, 5], [2, 1]]

                       X = [x, y]

                       B = [1, 3]

To find the solution using the matrix inversion method, we first find the inverse of matrix A and then multiply it with matrix B to get the values of x and y:

                  A^-1 = 1/det(A) * [[1, -5], [-2, 3]]

                      X = A^-1 * B

                          = (1/det(A)) * [[1, -5], [-2, 3]] * [1, 3]

                          = (1/det(A)) * [1-15, -2+9]

                          = (1/det(A)) * [-14, 7]

                          = [-7/det(A), 7/det(A)].

Here,

                  det(A) = 3 - 2*5 = -7,

So the inverse of matrix A is

                               (1/-7) * [[1, -5], [-2, 3]].

Thus, the solution to the system of linear equations is

                 x = -7/det(A) = 1, and

                 y = 7/det(A) = -1.

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Answer 2

Answer:

The solution for the system of linear equations 3x + 5y = 1 and 2x + y = 3 is x = -4 and y = 5.

Step-by-step explanation:

From the above question,

They have given :

Given equations are

3x + 5y - 1=0

2x + y3=0

The matrix form:

            | 3       5 |   | x |  = | 1 |

            | 2       1  | x | y | = | 3 |

Let A be the coefficient matrix:

             | 3    5 |

             | 2    1 |

Let X be the matrix of variables:

            | x |

            | y |

Let B be the matrix of constants:

            | 1 |

            | 3 |

The solution for X can be obtained using the formula:

           X = $A^{-1}$ * B

where  $A^{-1}$  is the inverse of A.

To find the inverse of A, we first need to calculate the determinant:

       det(A) = (3)(1) - (5)(2) = -7

Since the determinant is non-zero, A is invertible. We can find the inverse of A using the formula:

$A^{-1}$  = ($\frac{1}{del(A)}$)) * | d -b |

Substituting the values, we get:

            $A^{-1}$  = (1/-7) * | 1 -5 |

           | -2     3 |

Now we can calculate X:

X =  $A^{-1}$  * B

Substituting the values, we get:

           | x | | 1 -5 | | 1 | | -4 |

           | y | = | -2 3 | x | 3 | = | 5 |

The solution for the system of linear equations 3x + 5y = 1 and 2x + y = 3 is x = -4 and y = 5.

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