/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 9 Find the determinant of the matr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 9

Find the determinant of the matrix. $$\left[\begin{array}{ll} 2 & 6 \\ 0 & 3 \end{array}\right]$$

Short Answer

Expert verified
The determinant of the matrix is 6.

Step by step solution

01

Identifying the Matrix Elements

We have a 2x2 matrix given by \( \begin{bmatrix} 2 & 6 \ 0 & 3 \end{bmatrix} \). The main diagonal elements are 2 and 3, while the other diagonal elements are 6 and 0.
02

Applying the 2x2 Matrix Determinant Formula

Now, applying the formula for the determinant of a 2x2 matrix, which is calculated by subtracting the product of the off-diagonal elements from the product of the main diagonal elements. In other words, it's \( (a*d) - (b*c) \) where 'a' and 'd' are elements of the main diagonal (for the given matrix a=2, d=3) and 'b' and 'c' are the elements of the other diagonal (for the given matrix b=6, c=0).
03

Calculating the Determinant

Substituting the values, we have \( (2 * 3) - (6 * 0) \), which simplifies to 6. Hence, the determinant of this matrix is 6

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use Cramer's Rule to solve the system of linear equations, if possible. $$\begin{array}{l} 14 x_{1}-21 x_{2}-7 x_{3}=-21 \\ -4 x_{1}+2 x_{2}-2 x_{3}=2 \\ 56 x_{1}-21 x_{2}+7 x_{3}=7 \end{array}$$

If \(A\) is an idempotent matrix \(\left(A^{2}=A\right),\) then prove that the determinant of \(A\) is either 0 or 1

Find (a) the characteristic equation, (b) the eigenvalues, and (c) the corresponding eigenvectors of the matrix. $$\left[\begin{array}{ll} 2 & 1 \\ 3 & 0 \end{array}\right]$$

Use Cramer's Rule to solve the system of linear equations, if possible. $$\begin{array}{l} 13 x_{1}-6 x_{2}=17 \\ 26 x_{1}-12 x_{2}=8 \end{array}$$

Prove that if an \(n \times n\) matrix \(A\) is not invertible, then \(A[\operatorname{adj}(A)]\) is the zero matrix.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.