Let $ A = \begin{bmatrix} 2 & -1 \ -3 & -4 \end{bmatrix}$.Which of the following statements is correct?

Question

BlackTom AI · Accepted Answer

We start by restating the problem: given A = [ [2, -1], [-3, -4] ], determine which statement about the inverse is correct. The provided data shows that the claimed inverse is c. A^{-1} = [ [4/11, -1/11], [-3/11, -2/11] ].

First, compute the determinant of A to know if A is invertible. For a 2x2 matrix, det(A) = ad - bc where A = [ [a, b], [c, d] ]. Here a = 2, b = -1, c = -3, d = -4. So det(A) = (2)(-4) - (-1)(-3) = -8 - 3 = -11. Since det(A) ≠ 0, A is invertible, and the inverse exists.

Next, apply the standard formula for the inverse of a 2x2 matrix: A^{-1} = (1/det(A)) * [ [d, -b], [-c, a] ]. Substituting the values gives A^{-1} = (1/(-11)) * [ [-4, 1], [3, 2] ].

Carrying out the scalar multiplication yields A^{-1} = [ [(-4)/(-11), 1/(-11)], [3/(-11), 2/(-11)] ] = [ [4/11, -1/11], [-3/11, -2/11] ].

Thus, the reported inverse in option c matches the correct computation, confirming its accuracy.

Now, regarding the other options: note that the prompt provides only a single option (the one labeled c) and does not supply any alternative choices to evaluate. In a typical multiple-choice setting, one would compare each listed candidate against the actual inverse. Since no other options are given here, there is nothing to refute within this question as presented. The essential check—whether the matrix shown is indeed the inverse—has been performed and confirms correctness.

In summary, the determinant check confirms invertibility, the 2x2 inverse formula yields the matrix [ [4/11, -1/11], [-3/11, -2/11] ], and this matches the stated option c.

Let \( A = \begin{bmatrix} 2 & -1 \\ -3 & -4 \end{bmatrix}\).Which of the following statements is correct?

查看解析

登录即可查看完整答案

类似问题

Let \( A = \begin{bmatrix} 2 & -1 \\ -3 & -4 \end{bmatrix}\).Which of the following statements is correct?

The inverse of the matrix ( 1 0 1 4 2 0 𝑎 0 𝑎 2 ) is ( − 1 0 0.5 2 0.5 − 1 𝑎 2 0 − 0.5 ) . What is 𝑎 ?

If M=[1 0 0 0 1 0 6 3 1], then which of the following is M−1?

If \[M = \left [\begin{matrix}1 & 0 & 0\\-9 & 1 & 0\\6 & 2 & 1\end{matrix}\right ],\] then which of the following is \(M^{-1}\)?

If 𝑀 = [ 1 − 7 9 0 1 − 4 0 0 1 ] , then which of the following is 𝑀 − 1 ?

If \[M = \left [\begin{matrix}1 & -2 & 3\\0 & 1 & -1\\0 & 0 & 1\end{matrix}\right ],\] then which of the following is \(M^{-1}\)?

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