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Curl of a Vector Field
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Divergence of a Vector Field
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Gradient of a Scalar Field
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Properties of Transposes
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The Transpose of a Matrix
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Cartesian Coordinate
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Transform from Cartesian to Cylindrical Coordinate
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Transform from Cartesian to Spherical Coordinate
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Divergence Theorem/Gauss' Theorem
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Stokes' Theorem
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Definition of a Matrix
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Math Formulas
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Linear Algebra
> Matrix Addition
Matrix Addition
Two matrices may be added only if they have the same dimension; that is, they must have the same number of rows and columns. Addition is accomplished by adding corresponding elements.
For example, consider matrix
A
and matrix
B
.
Both matrices have the same number of rows and columns (3 rows and 3 columns), so they can be added. Thus,
And finally, note that the order in which matrices are added is not important, thus:
A
+
B
=
B
+
A
.
Example 1:
Add the two given matrices:
Solution:
Here the dimension of both the matrices is same, so we add the same.
Example 2:
What is the resultant when we add the two given matrices?
Solution:
As the dimension of both the matrices is same, we can add the corresponding entries to get the sum.
Example 3:
Solution:
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