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\integer{x=random(-10..10)}
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\integer{x=random(-10..10)}
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\integer{y=random(-10..10)}
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\integer{y=random(-10..10)}
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\real{norm=sqrt((\x)^2+(\y)^2)}
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\real{norm=sqrt((\x)^2+(\y)^2)}
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\statement{What is the length of the vector (\x,\y) in R<sup>2</sup>?}
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\statement{What is the length of the vector (\x,\y) in R<sup>2</sup>?}
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\hint{The length of a vector  (x,y) is equal to
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\hint{The length of a vector  (x,y) is equal to
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sqrt(x^2+y^2).}
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sqrt(x^2+y^2).}
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\answer{The length}{\norm}
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\answer{The length}{\norm}
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</pre>
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</pre>
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In this exercise, one has defined 2 random integers, x et y, who are the
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In this exercise, one has defined 2 random integers, x et y, who are the
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 to test it. (You can also copy the source into the menu under raw mode.)
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 to test it. (You can also copy the source into the menu under raw mode.)
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</li><li> <hr style="width:50%"/>
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</li><li> <hr style="width:50%"/>
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<b>Trace of matrix 2x2</b>, computes the trace of a matrix. The question
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<b>Trace of matrix 2x2</b>, computes the trace of a matrix. The question
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 is formatted by TeX, for a better presentation of the matrix. Here is
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 is formatted by TeX, for a better presentation of the matrix. Here is
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 the complete source of the exercise.
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 the complete source of the exercise.
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<pre>
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<pre>
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\title{Trace of matrix 2x2}
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\title{Trace of matrix 2x2}
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\language{en}
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\language{en}
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\computeanswer{yes}
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\computeanswer{yes}
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\format{tex}
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\format{html}
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\integer{range=20}
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\integer{range=20}
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\integer{a=random(-\range..\range)}
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\integer{a=random(-\range..\range)}
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\integer{b=random(-\range..\range)}
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\integer{b=random(-\range..\range)}
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\integer{c=random(-\range..\range)}
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\integer{c=random(-\range..\range)}
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\integer{d=random(-\range..\range)}
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\integer{d=random(-\range..\range)}
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\integer{trace=(\a)+(\d)}
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\integer{trace=(\a)+(\d)}
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\statement{Compute the trace of the matrix
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\statement{Compute the trace of the matrix
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$$\pmatrix{\a&\b\cr \c&\d}$$.}
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\([\a,\b;\c,\d]\).}
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\answer{The trace}{\trace}
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\answer{The trace}{\trace}
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</pre>
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</pre>
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We have first defined an integer ``range'', to be used to bound the
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We have first defined an integer ``range'', to be used to bound the
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random values a,b,c,d which are the elements of the matrix. And the trace is
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random values a,b,c,d which are the elements of the matrix. And the trace is
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of course defined by the sum of the elements on the diagonal. Please take
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of course defined by the sum of the elements on the diagonal. Please take
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care to the definition <span class="tt">trace=(\a)+(\d)</span>: the pairs of parentheses
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care to the definition <span class="tt">trace=(\a)+(\d)</span>: the pairs of parentheses
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are necessary, for the substitution is literary. If you define
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are necessary, for the substitution is literary. If you define
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<span class="tt">trace=\a+\d</span> and if a and d take the values of 3 and -15 respectively,
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<span class="tt">trace=\a+\d</span> and if a and d take the values of 3 and -15 respectively,
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you woule have <span class="tt">trace=3+-15</span>, a bad mathematical expression. <p>
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you woule have <span class="tt">trace=3+-15</span>, a bad mathematical expression. <p>
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Remark that in this exercise, the non-computed replies are admitted
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Remark that in this exercise, the non-computed replies are admitted
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(such as 2+15 or 3*105). <p>
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(such as 2+15 or 3*105). <p>
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You can
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You can
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!set parm=oef_answercnt=1&oef_choicecnt=0&oef_title=Trace of matrix 2x2&oef_format=tex&oef_computeanswer=yes&level=2&oef_parms=%5Cinteger%7Brange%3D20%7D%0D%0A%5Cinteger%7Ba%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Bb%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Bc%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Bd%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Btrace%3D%28%5Ca%29%2B%28%5Cd%29%7D&oef_statement=Compute the trace of the matrix%0D%0A%24%5Cpmatrix%7B%5Ca%26%5Cb%5Ccr %5Cc%26%5Cd%7D%24.&ansprompt1=The trace&ansgood1=%5Ctrace&oef_hint= &oef_solution= $
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!set parm=oef_answercnt=1&oef_choicecnt=0&oef_title=Trace of matrix 2x2&oef_format=html&oef_computeanswer=yes&level=2&oef_parms=%5Cinteger%7Brange%3D20%7D%0D%0A%5Cinteger%7Ba%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Bb%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Bc%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Bd%3Drandom%28-%5Crange..%5Crange%29%7D%0D%0A%5Cinteger%7Btrace%3D%28%5Ca%29%2B%28%5Cd%29%7D&oef_statement=Compute the trace of the matrix \\([\a,\b;\c,\d]\\).&ansprompt1=The trace&ansgood1=%5Ctrace&oef_hint= &oef_solution= $
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!href cmd=reply&mode=guided&$parm load this example into the menu
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!href cmd=reply&mode=guided&$parm load this example into the menu
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 to test it. (You can also copy the source into the menu under raw mode.)
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 to test it. (You can also copy the source into the menu under raw mode.)
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</li>
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</li>
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</ol>
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</ol>