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Each equation in Exercises $1-4$ illustrates a property of determinants. State the property.$$\left|\begin{array}{rrr}{1} & {3} & {-4} \\ {2} & {0} & {-3} \\ {3} & {-5} & {2}\end{array}\right|=\left|\begin{array}{rrr}{1} & {3} & {-4} \\ {0} & {-6} & {5} \\ {3} & {-5} & {2}\end{array}\right|$$

Adding any linear combination of rows into any row doesn't change the determinant.

Algebra

Chapter 3

Determinants

Section 2

Properties of Determinants

Introduction to Matrices

McMaster University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

00:47

Each equation in Exercises…

00:39

01:46

In Exercises 41–42, evalua…

02:02

The following exercises in…

01:00

01:29

Evaluate each determinant …

00:59

Determine whether each sta…

01:04

02:13

Evaluate the determinants.…

00:44

Compute the determinants i…

Okay, so we want to know how the property that makes these two determinants. So to do this, we first have to know how you go from the left matrix to the right matrix. It is the right operation that we did is right to you. Minus two times we rode one, and we put that into your tooth. So we use the property that if a multiple off one rode off a is added to another road to produce a matrix B, then determines be is it determines off, eh?

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In mathematics, the absolute value or modulus |x| of a real number x is its …

Each equation in Exercises $1-4$ illustrates a property of determinants. Sta…

In Exercises 41–42, evaluate each determinant.$$\left|\begin{array}{rr}{…

The following exercises investigate some of the properties of determinants. …

Evaluate each determinant in Exercises 23–28.$$\left|\begin{array}{rrr}{…

Determine whether each statement is true. Do not evaluate the determinants.<…

Evaluate the determinants.$\left|\begin{array}{rrrr}25 & 40 & 5 …

Compute the determinants in Exercises $1-8$ using a cofactor expansion acros…

06:45

In Exercises 27 and $28, A$ and $B$ are $n \times n$ matrices. Mark each sta…

00:41

In Exercises 19–24, justify each answer or construction.What is the rank…

06:02

In Exercises 11–16, compute the adjugate of the given matrix, and then use T…

02:01

In Exercises 39 and $40, A$ is an $n \times n$ matrix. Mark each statement T…

04:57

01:48

The set $\mathcal{B}=\left\{1-t^{2}, t-t^{2}, 2-2 t+t^{2}\right\}$ is a basi…

02:29

Suppose that all the entries in $A$ are integers and det $A=1 .$ Explain why…

01:33

Find the determinants in Exercises $15-20,$ where$$\left|\begin{arra…

Let $A$ be an $m \times n$ matrix, and let $\mathbf{u}$ and $\mathbf{v}$ be …

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