Real Analysis and Linear Transformation Fundamentals
Ms. A. Benazir, Assistant Professor of Mathematics, explains key concepts in Real Analysis such as linear combinations, spans, dimensions, and bases of vector spaces. Explore theorems and proofs regarding vector space dimensions.
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Presentation Transcript
What is a Matrix? MATRIX: A rectangular arrangement of numbers in rows and columns. The ORDER of a matrix is the number of the rows and columns. The ENTRIES are the numbers in the matrix. This order of this matrix is a 2 x 3. columns 5 6 2 1 2 0 rows
What is the order? 0 8 1 3 9 5 7 0 0 2 10 4 3 2 0 4 6 3 9 1 1 5 9 8 7 7 3 2 7 6 0 6 2 1 1 0
Adding Two Matrices To add two matrices, they must have the same order. To add, you simply add corresponding entries. + 4 + 5 ( ) 2 3 1 5 3 2 1 = + + ( 3 3 0 + 3 4 3 0 + + 0 4 7 ) 3 0 7 4 3 3 2 = 0 4 4 4
Subtracting Two Matrices To subtract two matrices, they must have the same order. You simply subtract corresponding entries. 9 2 4 4 0 7 ( 9 4 2 0 4 7 5 0 6 1 5 4 = ( 8 2 5 1 0 5 6 ) 4 1 3 8 2 3 2 1 ) 2 3 3 10 5 2 3 = 4 5 3 0 6
Multiplying a Matrix by a Scalar In matrix algebra, a real number is often called a SCALAR. To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar. 2 0 4 ( 4 ( 2 ) 4 ( 0 ) 4 = 4 1 4 ) 4 ( ) 1 16 8 0 = 4
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