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$21-28=$ Finding Determinants Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse. $$ \left[ \begin{array}{rrr}{2} & {1} & {0} \\ {0} & {-2} & {4} \\ {0} & {1} & {-3}\end{array}\right] $$

Name: Problem 21, Chapter 11: Algebra and Trigonometry
Uploaded: 2020-01-31T17:58:34-08:00
Duration: 1 min 34 s
Channel: Taylor Shimono
Description: 21-28= Finding Determinants Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse. [ 2 1 0 0 -2 4 0 1 -3 ]

   $21-28=$ Finding Determinants Find the determinant of the
matrix. Determine whether the matrix has an inverse, but don't
calculate the inverse.

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

Algebra and Trigonometry

James Stewart,… 4th Edition

Chapter 11, Problem 21

Instant Answer

Solved by Expert Taylor Shimono

01/31/2020

Step 1

The determinant of a 3x3 matrix can be calculated using the formula: det(A) = a(ei−fh)−b(di−fg)+c(dh−eg) where a, b, c are the elements of the first row, d, e, f are the elements of the second row, and g, h, i are the elements of the third row. Show more…

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$21-28=$ Finding Determinants Find the determinant of the matrix. Determine whether the matrix has an inverse, but don't calculate the inverse. $$ \left[ \begin{array}{rrr}{2} & {1} & {0} \\ {0} & {-2} & {4} \\ {0} & {1} & {-3}\end{array}\right] $$

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Key Concepts

Determinant

The determinant is a scalar value derived from a square matrix that encapsulates important algebraic properties of the matrix. It reflects factors such as volume scaling in linear transformations and whether the matrix is singular or non-singular. A nonzero determinant indicates a unique solution to the system of linear equations represented by the matrix, while a zero value signals a loss of invertibility.

Matrix Invertibility

Matrix invertibility refers to the ability to compute an inverse matrix, which is defined such that when multiplied with the original matrix, the result is the identity matrix. A key criterion for a matrix to have an inverse is that its determinant must be nonzero. This concept is essential in solving systems of equations and many applications in linear algebra.

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