Beginning & Intermediate Algebra (6th Edition)
Beginning & Intermediate Algebra (6th Edition)
6th Edition
ISBN: 9780134193090
Author: Elayn Martin-Gay
Publisher: PEARSON
Question
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Chapter E, Problem 1E
To determine

To find:

The value of the determinant:

35-17

Expert Solution & Answer
Check Mark

Answer to Problem 1E

Solution:

26

Explanation of Solution

Concept:

To find the value of a second order 2×2 determinant:

abcd=a×d-b×c=ad-bc

To find the value of a third order 3×3 determinant:

Step 1. Expand along the first row with signs alternatively + and -:

a1b1c1a2b2c2a3b3c3=a1b2c2b3c3-b1a2c2a3c3+c1a2b2a3b3

Step 2. Expand the second order minors to get the product:

a1b1c1a2b2c2a3b3c3=a1b2c3-b3c2-b1a2c3-a3c2+c1a2b3-a3b2

Step 3. Simplify further:

a1b1c1a2b2c2a3b3c3=a1b2c3-a1b3c2-b1a2c3+b1a3c2+c1a2b3-c1a3b2

Calculation:

35-17

The above is a second order 2×2 determinant.

So by the given concept, it can be expanded as:

35-17=3×7-5×-1

Simplify further:

35-17=21+5

35-17=26

Thus the value of the given determinant is 26.

Conclusion:

Therefore, the required value of the determinant is 26.

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