[math: U=[110234]V=[31]W=[0.60.50.40.5]X=[3546]Y=[132056001]]U = \left[ {\begin{array}{*{20}{c}}1&1&0\2&3&4\end{array}} ight]\,\,\;\quad V = \left[ {\begin{array}{*{20}{c}}3\1\end{array}} ight]\,\,\;\quad W = \left[ {\begin{array}{*{20}{c}}{0.6}&{0.5}\{0.4}&{0.5}\end{array}} ight]\;\,\,\;X = \left[ {\begin{array}{*{20}{c}}3&5\4&6\end{array}} ight]\quad \,\, \ Y = \left[ {\begin{array}{*{20}{c}}1&3&2\0&5&6\0&0&1\end{array}} ight]\;\quad det (W) =

Question

[math: U=[110234]V=[31]W=[0.60.50.40.5]X=[3546]Y=[132056001]]U = \left[ {\begin{array}{*{20}{c}}1&1&0\2&3&4\end{array}} ight]\,\,\;\quad V = \left[ {\begin{array}{*{20}{c}}3\1\end{array}} ight]\,\,\;\quad W = \left[ {\begin{array}{*{20}{c}}{0.6}&{0.5}\{0.4}&{0.5}\end{array}} ight]\;\,\,\;X = \left[ {\begin{array}{*{20}{c}}3&5\4&6\end{array}} ight]\quad \,\, \ Y = \left[ {\begin{array}{*{20}{c}}1&3&2\0&5&6\0&0&1\end{array}} ight]\;\quad det (W) =

BlackTom AI · Accepted Answer

Let's begin by restating the given data to focus our calculation: W is a 2x2 matrix with the entries W = [ [0.6, 0.5], [0.4, 0.5] ]. The determinant of a 2x2 matrix [ [a, b], [c, d] ] is computed as ad − bc. Applying this to W, we have a = 0.6, b = 0.5, c = 0.4, d = 0.5. Multiplying, ad = 0.6 × 0.5 = 0.30 and bc = 0.5 × 0.4 = 0.20. Subtracting these values gives det(W) = 0.30 − 0.20 = 0.10. Now, consider the answer option provided: 0.2. To assess its validity, compare it to the computed determinant. Since the actual determinant is 0.10, the option 0.2 does not match the true value. This indicates that the option is incorrect, and the discrepancy arises from a miscalculation or misreading of the matrix entries. If there were any additional answer choices, each would need to be evaluated in the same manner by calculating det(W) and checking consistency with each option. Also, note that the problem statement did not list other possible choices, so we cannot assess alternatives beyond the one shown. In summary, the determinant of W is 0.10, not 0.20, so the provided answer option is incorrect based on standard determinant computation, and a correct solution would reflect det(W) = 0.10.

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