LU BIBLE Math 101 Linear Algebra By: Abdulsalam
Shalashtein
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Row 1 Row 2 Column 1Column 2Column 3 Entries
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Lower TriangularUpper Triangular Diagonal Matrix
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Now for this part I will illustrate how to multiply matrices,
but this isnt to be used for proper mathematical writing this is
only to get y to understand the concept. Proceed to the next
slide.
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Here's how it works: Say the size of matrix A is 3 x 4 and the
size of matrix B is 4 x 1 and we want... Looking at the
sizes...
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I do these by stacking The answer goes here. Let's use these
matrices: Let's find :
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We just do an intersecting row and column thing: To fill this
spot, we multiply and add:
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Each entry in the answer matrix will work like this...
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So the answer is : Now Can we Multiply A B ?
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A matrix A is said to be invertible ( non-singular) if there
exists a matrix B where AB=BA=I n If A and B are invertible then :
(AB) -1 = B -1 A -1 A 1, , A r are (nxn) invertible matrices, then
A 1 x x A r is invertible and (A 1 x x A r )-1 = A r -1 x x A 1
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