
MATH 225A PROBLEMS OCTOBER 2, 2012 (1)
... (i) Show that T rL/K : L × L → K; (x, y) 7→ T rL/K (xy) is a non-degenerate, symmetric, K-bilinear form on L. (ii) Show that the map T rL/K : L → K; x 7→ T rL/K (x) is surjective. (Hint for both (i) and (ii): Artin’s theorem on linear independence of characters.) (4) Suppose that K is a number field ...
... (i) Show that T rL/K : L × L → K; (x, y) 7→ T rL/K (xy) is a non-degenerate, symmetric, K-bilinear form on L. (ii) Show that the map T rL/K : L → K; x 7→ T rL/K (x) is surjective. (Hint for both (i) and (ii): Artin’s theorem on linear independence of characters.) (4) Suppose that K is a number field ...
Relations and Functions
... f(x) means function of x and is read “f of x.” f(x) = 2x + 1 is written in function notation. The notation f(1) means to replace x with 1 resulting in the function value. f(1) = 2x + 1 ...
... f(x) means function of x and is read “f of x.” f(x) = 2x + 1 is written in function notation. The notation f(1) means to replace x with 1 resulting in the function value. f(1) = 2x + 1 ...
Relations and Functions
... f(x) means function of x and is read “f of x.” f(x) = 2x + 1 is written in function notation. The notation f(1) means to replace x with 1 resulting in the function value. f(1) = 2x + 1 ...
... f(x) means function of x and is read “f of x.” f(x) = 2x + 1 is written in function notation. The notation f(1) means to replace x with 1 resulting in the function value. f(1) = 2x + 1 ...
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... The prior discussion may already have helped some students to identify the rule is ‘6, +1’ and so it is relatively easy to work out A = 25, B = −17 (although a common misconception would be −19, with students subtracting the 1 rather than adding) and C = 1. Ask students their methods for finding th ...
... The prior discussion may already have helped some students to identify the rule is ‘6, +1’ and so it is relatively easy to work out A = 25, B = −17 (although a common misconception would be −19, with students subtracting the 1 rather than adding) and C = 1. Ask students their methods for finding th ...