AnswersGA-Advanced Algebra Concepts and Connections CRScalar and Matrix Multiplication

Determinants Answers

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1
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What is the correct formula for the value of the determinant?

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A
ab - cd
B
ab + cd
C
ad - cb
D
ad + cb
2
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Calculate the value for each determinant:=

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Answer:

9

3

Calculate the value for each determinant:=

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Answer:

-12

4

=

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Answer:

-8

5

=

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Answer:

1

6

= ⇒ 17

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Answer:

7

7

= ⇒ -48

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Answer:

72

8

What is the correct formula for calculating a 3 x 3 determinant?

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A
abc + def + ghi - adg - beh - cfi
B
adg + beh + cfh - abc - beh - cfi
C
aei + bfg + cdh - gec - hfa - idb
9

Calculate the value of the following determinants:= ⇒ 65

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Answer:

-25

10

=

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Answer:

162

11

Which of the following statements are true?

A
If any row of a square matrix is zero, its determinant is zero.
B
If all numbers in a matrix are equal, its determinant is zero.
C
The determinant of any identity matrix is zero.
D
The determinant of a matrix with all positive numbers is always positive.
E
The determinant of any zero matrix is zero.
12

Use the determinant of the coefficient matrix to determine which of the following linear systems have unique solutions.

A
Option
Option A
B
Option
Option B
C
Option
Option C
13

Calculate the area of the triangle:A =

Answer:

27

14

Consider the matrix:What is its determinant? Does the determinant depend on the variables? Make a conjecture.

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Answer:

The determinant of the matrix is 8. This is calculated by multiplying the diagonal elements (1 * 2 * 4 = 8) because the matrix is upper triangular. The determinant does not depend on the variables x, y, and z. I conjecture that when all elements below the main diagonal are zero, the determinant is always the product of the main diagonal elements.

15

Which of the following did your answer include?

A
The determinant is 8.
B
The determinant does not depend on the variables in the matrix.
C
When there are zeroes below the main diagonal, the determinant is the product of the diagonal.

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