Chapter 11: Q.33 (page 794)

In Problems $32$ and $33$ , use properties of determinants to find the value of each determinant if it is known thatrole="math" localid="1646935214028" $|\begin{matrix} x & y \\ a & b \end{matrix}| = 8$
$|\begin{matrix} y & x \\ b & a \end{matrix}|$

Short Answer

Expert verified

If $|\begin{matrix} x & y \\ a & b \end{matrix}| = 8$ , then the value of the determinant $|\begin{matrix} y & x \\ b & a \end{matrix}|$ is $- 8$ .

Step by step solution

Step 1. Given data

The given determinant is

$|\begin{matrix} x & y \\ a & b \end{matrix}| = 8$

The determinant whose value need to find out is

$|\begin{matrix} y & x \\ b & a \end{matrix}|$

Step 2. Value of determinant

According to properties of determinants, if any column of determinants is swiped with another column then the value of determinants will be negated.

$|\begin{matrix} y & x \\ b & a \end{matrix}|$ is obtained by swapping the first column with the second column of $|\begin{matrix} x & y \\ a & b \end{matrix}|$

so the value of the determinant $|\begin{matrix} y & x \\ b & a \end{matrix}|$ is negative of the value of the determinant $|\begin{matrix} x & y \\ a & b \end{matrix}|$

So $|\begin{matrix} x & y \\ a & b \end{matrix}| = 8 |\begin{matrix} y & x \\ b & a \end{matrix}| = - 8$

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In Problems $32$ and $33$ , use properties of determinants to find the value of each determinant if it is known thatrole="math" localid="1646935214028" $|\begin{matrix} x & y \\ a & b \end{matrix}| = 8$
$|\begin{matrix} y & x \\ b & a \end{matrix}|$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Value of determinant

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In Problems 32and33, use properties of determinants to find the value of each determinant if it is known thatrole="math" localid="1646935214028" xyab=8yxba

Short Answer

Step by step solution

Step 1. Given data

Step 2. Value of determinant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Probability and Statistics

Pure Maths

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problems $32$ and $33$ , use properties of determinants to find the value of each determinant if it is known thatrole="math" localid="1646935214028" $|\begin{matrix} x & y \\ a & b \end{matrix}| = 8$
$|\begin{matrix} y & x \\ b & a \end{matrix}|$