ai calculator learanadeAI

Symmetric Matrices Calculator

Ask and get solution to your homeworkAsk now and get step-by-step solutions
Get Solution
Example
Created on 2024-06-20Asked by Michael Mitchell (Solvelet student)
Determine if the matrix A=(123245356) A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{pmatrix} is symmetric.

Solution

To determine if the matrix A=(123245356) A = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{pmatrix} is symmetric: 1. **Definition of symmetric matrix:** A matrix AA is symmetric if A=ATA = A^T, where ATA^T is the transpose of AA. 2. **Compute the transpose ATA^T:** AT=(123245356). A^T = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{pmatrix}. 3. **Compare AA with ATA^T:** A=AT. A = A^T. 4. **Result:** Since A=ATA = A^T, the matrix AA is symmetric. Solved on Solvelet with Basic AI Model
Some of the related questions asked by Jack Green on Solvelet
1. Determine if the matrix A=[1223]A = \begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix} is symmetric.2. Find the eigenvalues and eigenvectors of the symmetric matrix B=(4−1−14) B = \begin{pmatrix} 4 & -1 \\ -1 & 4 \end{pmatrix} .,
DefinitionA symmetric matrix is ​​a square matrix for which A=AT. These matrices have important properties such as real eigenvalues ​​and orthogonal eigenvectors. (21)(32) is symmetric, e.g. (12)(23)
Related Calculators
Composite Functions CalculatorComplex Numbers CalculatorStokes Theorem CalculatorApplications of Integrals Calculator
@Copyright Solvelet 2024Privacy PolicyTerms and Condition