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

Question

BlackTom AI · Accepted Answer

The problem asks which statement about the matrix A is correct, where A = [[2, -1], [-3, -4]].

First, I will compute the inverse of A to verify the given candidate. For a 2x2 matrix A = [[a, b], [c, d]], the inverse, if it exists, is (1/det(A)) * [[d, -b], [-c, a]] where det(A) = ad - bc.

Here, a = 2, b = -1, c = -3, d = -4.
- Compute the determinant: det(A) = (2)(-4) - (-1)(-3) = -8 - 3 = -11.
- The adjugate (the matrix [[d, -b], [-c, a]]) is [[-4, 1], [3, 2]].
- Multiply by 1/det(A) = -1/11: A^{-1} = (-1/11) * [[-4, 1], [3, 2]] = [[4/11, -1/11], [-3/11, -2/11]].

Now, compare with the provided statement: c. A^{-1} = [[4/11, -1/11], [-3/11, -2/11]]. This matches exactly the computed inverse.

Since the question lists only option c as the correct one and no other options are provided to evaluate, we cannot analyze other choices. However, the key step is verifying the inverse via the standard formula for a 2x2 matrix, which confirms the given inverse is correct. The result also aligns with the determinant being -11 and the corresponding scaled adjugate.

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

View Explanation

Log in for full answers

Similar Questions

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 \(M^{-1}\)?

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler