Download Introduction to Matrix Algebra by Autar Kaw PDF

By Autar Kaw

This booklet is written essentially for college kids who're * at freshman point or * don't take a whole path in Linear/Matrix Algebra, or * short of a latest and utilized method of Matrix Algebra.

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Sample text

B. linearly dependent. 5. If a set of vectors is linearly independent, a subset of the vectors is A. linearly independent. B. linearly dependent. 6. If a set of vectors is linearly dependent, then A. at least one vector can be written as a linear combination of others. B. At least one vector is a null vector. 7. If the dimension of a set of vectors is less than the number of vectors in the set, then the set of vectors is A. linearly dependent. B. linearly independent. 8. 9. 5) r r r If u , v , w are three nonzero vector of 2-dimensions, then A.

Two matrices [A] and [B] can be added only if they are the same size, then the addition is shown as [C] = [A] + [B] where cij = aij + bij _________________________________ Example Add two matrices [A] =  5 2 3  1 2 7  6 7 − 2  3 5 19  [B] =  Solution [C ] = [A] + [B] Introduction to Matrix Algebra – Copyright – Autar K Kaw - 34- 5 2 3 6 7 − 2 = +  1 2 7  3 5 19  5 + 6 2 + 7 3 − 2  =  1 + 3 2 + 5 7 + 19 11 9 1  =   4 7 26 _________________________________ Example Blowout r’us store has two locations ‘A’ and ‘B’, and their sales of tires are given by make (in rows) and quarters (in columns) as shown below.

Since aii = -aii only if aii = 0, all the diagonal elements of a skew symmetric matrix have to be zero. Trace of a matrix: The trace of a nxn matrix [A] is the sum of the diagonal entries of [A], that is, n tr [ A] = ∑ a ii i =1 _________________________________ Example Find the trace of 15 6 7 [A] =  2 − 4 2  3 2 6 Solution tr [ A] = ∑ a ii 3 i =1 = (15) + (−4) + (6) = 17 _________________________________ Introduction to Matrix Algebra – Copyright – Autar K Kaw - 49- Example The sale of tires are given by make (rows) and quarters (columns) for Blowout r’us store location A.

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