Evaluate each determinant in Exercises 1–10.

Question

Evaluate each determinant in Exercises 1–10. $\begin{vmatrix}\frac{1}{2} & \frac{1}{2} \\frac{1}{8} & - \frac{3}{4}\end{vmatrix}$

Accepted Answer

Welcome back, I am so glad you're here. We are given this matrix going to rewrite it. It is going down the first column 1 5th 7/10 in the second column five halves and negative three halves and we are asked to evaluate the second order determinant. Alright, we recall from previous lessons on second order determinants that we're going to take the term in the upper left hand corner and multiply it by the term in the bottom right hand corner. So 1/5 times negative three halves is negative 3/10. And then we are going to take the term in the bottom left hand corner and multiply by the term in the upper right hand corner. So that's 7/10 times five halves which is 35 20th. So and then we are going to subtract the two terms from each other. So starting with the first one, negative 3/10 minus the 2nd 1. 35 20th. And because we have two fractions they need to have a common denominator. Let's multiply the first one times two over to to get a common denominator of 20. So two times negative three is negative 6/ -35 20th. And now because we have a common denominator we can just do the subtraction in the numerator. So excuse me in the numerator negative six minus 35 is negative 41 over the common denominator of 20. So our determinant is negative 41 20th. So we look at our answer choices in this matches with answer choice. A well done. We'll catch you on the next one

Evaluate each determinant in Exercises 1–10. $\begin{vmatrix}\frac{1}{2} & \frac{1}{2} \\\frac{1}{8} & - \frac{3}{4}\end{vmatrix}$

Key Concepts

Determinant of a 2x2 Matrix

Fraction Arithmetic

Simplification of Expressions

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