1. (20 points) Write a VBA code that can find the determinant of any size matrix

Question

1. (20 points) Write a VBA code that can find the determinant of any size matrix that is given by user.

3. (30 points) Develop a VBA program that can solve a problem like question 2 using LU decomposition with the input values read from the spreadsheet by your program.

Questions 2:

Solve the following linear system of equations:

2x1- 6x2 - x3 = -38

-3x1- x2 +7x3 = -34

-8x1 + x2 -2x3 = -20

I've solved the linear system but i have the problem with the VBA part. I don't really know what should i write in the VBA in excel, Hope you can help, thank you very much.

Explanation / Answer

    Public Function Det(ByRef a(,) As Double, ByVal n As Integer) As Double
        If Not Math.Sqrt(a.Length) - 1 = n Then
            Throw New Exception("Error, size is not correct")
            Exit Function
        End If
        Dim Result As Double = 0
        If n = 1 Then Return a(1, 1)
        If n = 2 Then Return a(1, 1) * a(2, 2) - a(2, 1) * a(1, 2)
        Dim b(n - 1, n - 1) As Double
        For i As Integer = 1 To n
            For j As Integer = 1 To n - 1
                For k As Integer = 1 To n - 1
                    If k >= i Then
                        b(j, k) = a(j + 1, k + 1)
                    Else
                        b(j, k) = a(j + 1, k)
                    End If
                Next
            Next
            Result += ((-1) ^ (i + 1)) * a(1, i) * Det(b, n - 1)
        Next
        Return Result
    End Function

Here is an example how to use this function:

        Dim Size As Integer = 3
        Dim a(Size, Size) As Double
        a(1, 1) = 1
        a(1, 2) = 2
        a(1, 3) = 3
        a(2, 1) = 4
        a(2, 2) = -5
        a(2, 3) = 6
        a(3, 1) = 7
        a(3, 2) = 8
        a(3, 3) = 9
        Dim R As Double = Det(a, 3)

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