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Curl of a Vector Field
Divergence of a Vector Field
Gradient of a Scalar Field
Properties of Transposes
The Transpose of a Matrix
Transform from Cartesian to Cylindrical Coordinate
Transform from Cartesian to Spherical Coordinate
Transform from Cylindrical to Cartesian Coordinate
Transform from Spherical to Cartesian Coordinate
Divergence Theorem/Gauss' Theorem
Definition of a Matrix
> Properties of the Identity Matrix
Properties of the Identity Matrix
A matrix multiplied by its inverse is equal to the identity matrix.
A = I
All the elements of the matrix apart from the diagonal are zero.
For an m × n matrix
A = A I
, then find
M × I
is an identity matrix.
is square matrix of order 2×2, the identity matrix
needs to be of the same order 2×2. [Rule for Matrix Multiplication.]
Determine the value of x, y and z if:
On the L.H.S we have:
Now, we compare the L.H.S matrix with the R.H.S matrix in order to determine the values of x, y and z.
y = 4x ……….(1)
z – 1 = 6 ……(2)
x – 2 = y/2 ……(3)
From (2) we can determine the value of z, which is z = 7.
From (3) we can simplify the equation to y = 2x – 4
We now have two equations with two unknown factors, namely x and y:
y = 2x – 4
y = 4x
To determine the value of x and y, simply insert y = 4x into y = 2x – 4, which will give us:
4x = 2x – 4 => x = – 2
And y = 4x = – 8
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