Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 1

The matrix, \(H\), is defined by $$ H=\left(\begin{array}{cc} 2 & 1 \\ \alpha & 0 \\ -3 & \beta \end{array}\right) $$ (a) State the size of \(H\). (b) State \(h_{11}, h_{21}, h_{32}\)

Short Answer

Expert verified
Answer: The size of matrix H is 3 x 2. The values of h_{11} = 2, h_{21} = α, and h_{32} = β.

Step by step solution

01

Determine the size of the matrix H

To find the size of the matrix, count the number of rows and columns. The given matrix H has 3 rows and 2 columns. The size of the matrix \(H\) can be represented as \(3 \times 2\).
02

Identify the values of h_{11}, h_{21} and h_{32}

The elements in a matrix are usually denoted by their row index and column index (respectively). For example, \(h_{11}\) is the element found in the first row and the first column. Using this convention, - \(h_{11}\) is the element in the 1st row and 1st column, which is 2. - \(h_{21}\) is the element in the 2nd row and 1st column, which is \(\alpha\). - \(h_{32}\) is the element in the 3rd row and 2nd column, which is \(\beta\).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Refer to matrices \(A, B\) and \(C\) where $$ A=\left(\begin{array}{cc} 3 & 1 \\ -1 & 2 \end{array}\right), \quad B=\left(\begin{array}{ccc} 1 & 4 & 0 \\ 2 & 7 & -1 \end{array}\right), \quad C=\left(\begin{array}{cc} -2 & 1 \\ 4 & -1 \\ 0 & 3 \end{array}\right) $$ Calculate the following products. \(A B\)

Given $$ A=\left(\begin{array}{ll} 6 & 1 \\ 3 & 7 \end{array}\right) $$ state (a) \(A-2 I_{2}\) (b) \(A-\lambda I_{2}\) where \(\lambda\) is a constant.

State the transpose of \(I_{3}\).

State the number of elements in an \(n \times m\) matrix.

If \(A\) is a matrix, state conditions on \(A\) for \(A^{2}\) to exist.
See all solutions

Recommended explanations on Physics Textbooks

Force

Read Explanation

Rotational Dynamics

Read Explanation

Waves Physics

Read Explanation

Famous Physicists

Read Explanation

Electromagnetism

Read Explanation

Thermodynamics

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.

Sign-up for free