Matrices - Notes and practice materials on Engineering Maths PDF

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Notes and practice materials on Engineering Maths...

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Matrices

Determinant & Inverse of a 2x2 Matrix The determinant of a 2x2 matrix:

Minors & Cofactors  

There is a matrix minor corresponding to each element of a matrix The minor is calculated by o ignoring the values on the current row and column o calculate the determinant of the remaining 2x2 matrix

Example:

The minor of the top left corner is:

The cofactor is the minor multiplied by it's correct sign. The signs form a checkerboard pattern:

The matrix of cofactors is denoted C.

Determinant of a 3x3 Matrix The determinant of a 3x3 matrix is calculated by multiplying each element in one row/column by it's cofactor, then summing them. For the matrix:

This shows the expansion of the top row, but any column or row will produce the same result.

Inverse of a 3x3 Matrix 

Calculate matrix of minors Calculate matrix of cofactors C



Transpose CT



Multiply by 1 over determinant



The transposed matrix of cofactors CT is therefore:

Explanding by the bottom row to calculate the determinant (it has 2 zeros so easy calculation):

detM=0×0+1×10+0×0=10...