$U = \left[ {\begin{array}{*{20}{c}}1&1&0\2&3&4\end{array}} \right]\,\,\;\quad V = \left[ {\begin{array}{*{20}{c}}3\1\end{array}} \right]\,\,\;\quad W = \left[ {\begin{array}{*{20}{c}}{0.6}&{0.5}\{0.4}&{0.5}\end{array}} \right]\;\,\,\;X = \left[ {\begin{array}{*{20}{c}}3&5\4&6\end{array}} \right]\quad \,\, \ Y = \left[ {\begin{array}{*{20}{c}}1&3&2\0&5&6\0&0&1\end{array}} \right]\;\quad $ det (W) =

Question

BlackTom AI · Accepted Answer

We are given the 2x2 matrix W = [[0.6, 0.5], [0.4, 0.5]] and asked for det(W).
First, recall the formula for the determinant of a 2x2 matrix [[a, b], [c, d]]: det = ad − bc.

Option a: -0.5. If we plug a = 0.6, b = 0.5, c = 0.4, d = 0.5 into ad − bc, we get (0.6)(0.5) − (0.5)(0.4) = 0.30 − 0.20 = 0.10, not -0.5. This shows this choice is incorrect.

Option b: 0.5. Using the same calculation ad − bc = 0.30 − 0.20 = 0.10, we see the actual determinant is 0.10, not 0.5. Therefore this option is also incorrect.

Option c: 0.1. This matches the computed value: 0.30 − 0.20 = 0.10, which is 0.1 when written in decimal form. Hence this option is consistent with the determinant formula.

Option d: 0.2. Since the exact calculation yields 0.10, not 0.2, this option is inaccurate.

Option e: not defined. The determinant of a 2x2 matrix is always defined (provided the entries are real numbers, which they are here), so claiming 'not defined' is incorrect.

Summarizing the checks, only option c yields the correct determinant value 0.1, while all other options either miscalculated the result or misunderstand the determinant's existence for a 2x2 matrix.

MCD1550 / MCD2140 - T1 - 2025 TEST 2 (Week 6)

查看解析

登录即可查看完整答案

类似问题

Define the matrix M=[4 1 −4 −2 x−4 −1 0 3 −1]. Which of the following is detM?

Define the matrix \[M = \left [\begin{matrix}1 & -5 & 1\\3 & 0 & x + 6\\2 & 3 & -5\end{matrix}\right ] .\] Which of the following is \(\operatorname {det}{M}\)?

Evaluate \left| \begin{array}{cc} 4 & -2 \\ 3 & 2 \end{array} \right| .

Practice question 5 In this question, you will test your knowledge of calculating determinants Find the determinant, to 2 d.p., of the following matrix: \; \;\left(\begin{array}{cc} 2 & 3\\ 3 & 4 \end{array}\right)

The matrix [x−1−3x+1−2] \left[\begin{array}{cc} x-1&-3 \\ x+1&-2 \end{array}\right] will NOT have an inverse where:

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单