Question

$15-20=$ Minors and Cofactors Evaluate the minor and cofactor using the matrix $A .$ $$A=\left[ \begin{array}{rrr}{1} & {0} & {\frac{1}{2}} \\ {-3} & {5} & {2} \\ {0} & {0} & {4}\end{array}\right]$$ $$ M_{11}, A_{11} $$

Name: Problem 15, Chapter 11: Algebra and Trigonometry
Uploaded: 2020-01-31T17:49:59-08:00
Duration: 1 min 21 s
Channel: Taylor Shimono
Description: 15-20= Minors and Cofactors Evaluate the minor and cofactor using the matrix A . A=[ 1 0 (1)/(2) -3 5 2 0 0 4 ] M11, A11

   $15-20=$ Minors and Cofactors Evaluate the minor and cofactor
using the matrix $A .$

$$A=\left[ \begin{array}{rrr}{1} & {0} & {\frac{1}{2}} \\ {-3} & {5} & {2} \\ {0} & {0} & {4}\end{array}\right]$$

$$
M_{11}, A_{11}
$$

Algebra and Trigonometry

James Stewart,… 4th Edition

Chapter 11, Problem 15

Instant Answer

Solved by Expert Taylor Shimono

01/31/2020

Step 1

To do this, we cross out the first row and the first column of the matrix $A$ because the indices of $M_{11}$ are 1 and 1. This leaves us with the submatrix: $$\left[ \begin{array}{rr}{5} & {2} \\ {0} & {4}\end{array}\right]$$ Show more…

Show all steps

Thanks for your feedback!

$15-20=$ Minors and Cofactors Evaluate the minor and cofactor using the matrix $A .$ $$A=\left[ \begin{array}{rrr}{1} & {0} & {\frac{1}{2}} \\ {-3} & {5} & {2} \\ {0} & {0} & {4}\end{array}\right]$$ $$ M_{11}, A_{11} $$

Play audio

Feedback

Taylor Shimono and 77 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Cofactor of a Matrix Element

A cofactor is obtained by multiplying the minor by (-1) raised to the sum of the row and column indices of the element. Cofactors retain the sign pattern necessary for correct expansion in determinant calculations and play a crucial role in computing the inverse of a matrix.

Determinant of a 2x2 Matrix

The determinant of a 2x2 matrix is calculated using the formula ad - bc, where a, b, c, and d are the elements of the matrix. This calculation is essential when evaluating minors that reduce a larger matrix to a 2x2 submatrix.

Minor of a Matrix Element

A minor of a matrix element is the determinant of the submatrix formed by removing the row and the column of that element. It is a fundamental concept used in various matrix computations, such as evaluating determinants and developing the cofactor expansion method.

Please give Ace some feedback