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assign5_soln

# assign5_soln - Math 136 Assignment 5 Solutions 1 Calculate...

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Math 136 Assignment 5 Solutions 1. Calculate the following products or explain why the product is not defined. (a) 1 0 - 2 1 1 2 3 4 - 3 1 3 3 Solution: Since the number of columns of the first matrix does not equal the number of rows of the second matrix, the product is not defined. (b) 2 2 - 2 0 1 0 0 1 - 2 2 1 1 2 3 3 Solution: 2 2 - 2 0 1 0 0 1 - 2 2 1 1 2 3 3 = 0 0 1 2 - 5 - 4 (c) 3 1 2 2 1 5 Solution: 3 1 2 2 1 5 = 17 (d) 2 1 5 3 1 2 Solution: 2 1 5 3 1 2 = 6 2 4 3 1 2 15 5 10 2. Prove that if A, B, C M m × n ( R ) and s, t R are scalars, then a) A + ( B + C ) = ( A + B ) + C . Solution: We have ( A + ( B + C ) ) ij = A ij + ( B + C ) ij = A ij + ( ( B ) ij + ( A ) ij ) = ( ( A ) ij + ( B ) ij ) + ( C ) ij = ( A + B ) ij + C ij = ( ( A + B ) + C ) ij 1

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2 b) ( s + t ) A = sA + tA . Solution: We have ( ( s + t ) A ) ij = ( s + t )( A ) ij = s ( A ) ij + t ( A ) ij = ( sA ) ij + ( tA ) ij = ( sA + tA ) ij 3. Prove that each of the following mappings are linear and find the standard matrix of the mapping.
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assign5_soln - Math 136 Assignment 5 Solutions 1 Calculate...

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