Question

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

Name: Problem 24, Chapter 10: Precalculus Mathematics for Calculus
Uploaded: 2020-05-27T18:16:05-08:00
Duration: 54 s
Channel: Bahar Tehranipoor
Description: Find the determinant of the matrix. Determine whether the matrix has an inverse, but don’t calculate the inverse. [ -2 -(3)/(2) (1)/(2) 2 4 0 (1)/(2) 2 1 ]

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

Precalculus Mathematics for Calculus

James Stewart,… 7th Edition

Chapter 10, Problem 24

Instant Answer

Solved by Expert Bahar Tehranipoor

05/27/2020

Step 1

We can do this by using the formula for the determinant of a 3x3 matrix, which involves the cross multiplication of the elements of the matrix. Show more…

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

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Key Concepts

Determinant

The determinant is a scalar value computed from a square matrix that summarizes certain properties of the linear transformation represented by the matrix, such as scaling effects on area or volume. It is also an indicator of the matrix’s invertibility; if the determinant is zero, the matrix is said to be singular (noninvertible), while a nonzero determinant means the matrix is nonsingular (invertible).

Matrix Inverse

The inverse of a matrix is another matrix that, when multiplied with the original, yields the identity matrix. A matrix has an inverse if and only if its determinant is nonzero. This concept is pivotal because it relates to solving systems of linear equations and understanding the behavior of linear transformations.

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