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Find the determinants in Exercises $15-20,$ where$$\left|\begin{array}{ccc}{a} & {b} & {c} \\ {d} & {e} & {f} \\ {g} & {h} & {i}\end{array}\right|=7$$$$\left|\begin{array}{ccc}{a} & {b} & {c} \\ {2 d+a} & {2 e+b} & {2 f+c} \\ {g} & {h} & {i}\end{array}\right|$$

14

Algebra

Chapter 3

Determinants

Section 2

Properties of Determinants

Introduction to Matrices

Campbell University

McMaster University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

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Find the determinants in E…

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Determine whether each sta…

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Given that$$\left|…

were given a matrix and the value of the determinant and were asked to find the determinant of this matrix, our Matrix's ABC, two d plus A to E plus B two F plus C and G H I. And we're told that the determinant of the Matrix A B C, D e f g h i. Is seven. To find the determinant of this matrix notice that we have added he first wrote to the second row. And so one of the properties of the determinants says that this is equal to the determinant of the Matrix a B, C two d to e two f g h i. And now notice that we can factor out a two from the second row and another property. The determinants tells us that this is two times the determinant of the Matrix ABC D e f g h i. And you know this is two times seven or 14 and this is our answer

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