In Exercises 1–8 , evaluate the determinant of the given matrix by ( a ) cofactor expansion and ( b ) using elementary row operations to intro-duce zeros into the matrix. [ − 4 2 3 3 ]

Question

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Answer 1

Textbook Question

Chapter 2, Problem 1SE

In Exercises 1–8, evaluate the determinant of the given matrix by (a) cofactor expansion and (b) using elementary row operations to intro-duce zeros into the matrix.

[ − 4 2 3 3 ]

(a)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using cofactor expansion.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

Definition used:

Determinant:

“The determinant of a matrix A=[abcd] is given by the formula ad−bc and the matrix A is said to be invertible if, ad−bc≠0.”

Calculation:

The given matrix is A=[−4233].

Use cofactor expansion and obtain the value of the determinant as shown below.

det(A)=(−4)⋅3−2⋅3=−12−6=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

(b)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using elementary row operations.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

The given matrix is A=[−4233].

Obtain the value of the determinant as shown below.

|A|=|−4233| (R2→R23)~3⋅|−4211| (R1→R1+4R2)~3⋅|0611| (R2→R2−16R1)~3⋅|0610|

On further simplifications,

|A|=3⋅(−6)=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

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Answer 2

Textbook Question

Chapter 2, Problem 1SE

In Exercises 1–8, evaluate the determinant of the given matrix by (a) cofactor expansion and (b) using elementary row operations to intro-duce zeros into the matrix.

[ − 4 2 3 3 ]

(a)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using cofactor expansion.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

Definition used:

Determinant:

“The determinant of a matrix A=[abcd] is given by the formula ad−bc and the matrix A is said to be invertible if, ad−bc≠0.”

Calculation:

The given matrix is A=[−4233].

Use cofactor expansion and obtain the value of the determinant as shown below.

det(A)=(−4)⋅3−2⋅3=−12−6=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

(b)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using elementary row operations.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

The given matrix is A=[−4233].

Obtain the value of the determinant as shown below.

|A|=|−4233| (R2→R23)~3⋅|−4211| (R1→R1+4R2)~3⋅|0611| (R2→R2−16R1)~3⋅|0610|

On further simplifications,

|A|=3⋅(−6)=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

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Answer 3

Textbook Question

Chapter 2, Problem 1SE

In Exercises 1–8, evaluate the determinant of the given matrix by (a) cofactor expansion and (b) using elementary row operations to intro-duce zeros into the matrix.

[ − 4 2 3 3 ]

(a)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using cofactor expansion.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

Definition used:

Determinant:

“The determinant of a matrix A=[abcd] is given by the formula ad−bc and the matrix A is said to be invertible if, ad−bc≠0.”

Calculation:

The given matrix is A=[−4233].

Use cofactor expansion and obtain the value of the determinant as shown below.

det(A)=(−4)⋅3−2⋅3=−12−6=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

(b)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using elementary row operations.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

The given matrix is A=[−4233].

Obtain the value of the determinant as shown below.

|A|=|−4233| (R2→R23)~3⋅|−4211| (R1→R1+4R2)~3⋅|0611| (R2→R2−16R1)~3⋅|0610|

On further simplifications,

|A|=3⋅(−6)=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

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Answer 4

Textbook Question

Chapter 2, Problem 1SE

In Exercises 1–8, evaluate the determinant of the given matrix by (a) cofactor expansion and (b) using elementary row operations to intro-duce zeros into the matrix.

[ − 4 2 3 3 ]

(a)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using cofactor expansion.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

Definition used:

Determinant:

“The determinant of a matrix A=[abcd] is given by the formula ad−bc and the matrix A is said to be invertible if, ad−bc≠0.”

Calculation:

The given matrix is A=[−4233].

Use cofactor expansion and obtain the value of the determinant as shown below.

det(A)=(−4)⋅3−2⋅3=−12−6=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

(b)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using elementary row operations.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

The given matrix is A=[−4233].

Obtain the value of the determinant as shown below.

|A|=|−4233| (R2→R23)~3⋅|−4211| (R1→R1+4R2)~3⋅|0611| (R2→R2−16R1)~3⋅|0610|

On further simplifications,

|A|=3⋅(−6)=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

(a)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using cofactor expansion.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

Definition used:

Determinant:

“The determinant of a matrix A=[abcd] is given by the formula ad−bc and the matrix A is said to be invertible if, ad−bc≠0.”

Calculation:

The given matrix is A=[−4233].

Use cofactor expansion and obtain the value of the determinant as shown below.

det(A)=(−4)⋅3−2⋅3=−12−6=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

(b)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using elementary row operations.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

The given matrix is A=[−4233].

Obtain the value of the determinant as shown below.

|A|=|−4233| (R2→R23)~3⋅|−4211| (R1→R1+4R2)~3⋅|0611| (R2→R2−16R1)~3⋅|0610|

On further simplifications,

|A|=3⋅(−6)=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

Answer 8

(a)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using cofactor expansion.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

Definition used:

Determinant:

“The determinant of a matrix A=[abcd] is given by the formula ad−bc and the matrix A is said to be invertible if, ad−bc≠0.”

Calculation:

The given matrix is A=[−4233].

Use cofactor expansion and obtain the value of the determinant as shown below.

det(A)=(−4)⋅3−2⋅3=−12−6=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

The determinant of the matrix A=[−4233], using cofactor expansion.

Answer 13

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Answer 14

Explanation of Solution

Definition used:

Determinant:

“The determinant of a matrix A=[abcd] is given by the formula ad−bc and the matrix A is said to be invertible if, ad−bc≠0.”

Calculation:

The given matrix is A=[−4233].

Use cofactor expansion and obtain the value of the determinant as shown below.

det(A)=(−4)⋅3−2⋅3=−12−6=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

Answer 15

(b)

Expert Solution

To determine

The determinant of the matrix A=[−4233], using elementary row operations.

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Explanation of Solution

The given matrix is A=[−4233].

Obtain the value of the determinant as shown below.

|A|=|−4233| (R2→R23)~3⋅|−4211| (R1→R1+4R2)~3⋅|0611| (R2→R2−16R1)~3⋅|0610|

On further simplifications,

|A|=3⋅(−6)=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

The determinant of the matrix A=[−4233], using elementary row operations.

Answer 20

Answer to Problem 1SE

The determinant of the matrix A=[−4233] is −18_.

Answer 21

Explanation of Solution

The given matrix is A=[−4233].

Obtain the value of the determinant as shown below.

|A|=|−4233| (R2→R23)~3⋅|−4211| (R1→R1+4R2)~3⋅|0611| (R2→R2−16R1)~3⋅|0610|

On further simplifications,

|A|=3⋅(−6)=−18

Thus, the determinant of the matrix A=[−4233] is −18_.

Answer 22

In Exercises 1–8 , evaluate the determinant of the given matrix by ( a ) cofactor expansion and ( b ) using elementary row operations to intro-duce zeros into the matrix. [ − 4 2 3 3 ]

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Answer to Problem 1SE

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Answer to Problem 1SE

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