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

Want to see more full solutions like this?

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_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

A craftsman of string instruments has received a new order to craft violins and guitars. The craftsman haslimited resources (wood, string, varnish) and time available to create the instruments. Each type of instrument(violin and guitar) requires specific amounts of these resources as well as a certain amount of time to complete.The craftsman wants to find the optimal number of violins and guitars to create in order to maximize the profitfrom selling them, while respecting the resource and time constraints (all instruments will be sold).The profit from selling each violin is 6,000 NOK, and the profit from selling each guitar is 3,000 NOK.Each violin requires 4 kg of wood, 0.3 l of varnish, and 2 m of string, and takes 3 days to craft. For eachguitar, the craftsman needs 5 kg of wood, 0.1 l of varnish, and 6 m of string, and it takes 2 days to make it.The craftsman’s workshop is stocked with 60 kg of wood, 2.5 l of varnish, and 65 m of string. The order needsto be completed in 30…

C Clever | Portal x ALEKS - Marisa Haskins - Le Marisa Haskins - Essay Temp x Earth and Space 2 Desmos | Graphing Calculator x cwww-awy.aleks.com/alekscgi/x/Isl.exe/10_u-IgNslkr7j8P3JH-IQ2_KWXW3dyps2nJxZ_kvzXfsB26H8ZG13mFzq9lmGAYN JJOEyt0CsUr4AMXmcIVNqw-dNsEi_PzyC7v ◇ Exponents and Exponential Functions Finding the final amount in a word problem on compound interest 0/5 Ma John deposited $4000 into an account with 4.6% interest, compounded annually. Assuming that no withdrawals are made, how much will he have in the account after 7 years? Do not round any intermediate computations, and round your answer to the nearest cent. $0 Explanation Check 1 ! 12 Q W # 3 品: S חח E $ SA 4 4 a R 5775 % e MacBook Air ৫ Di F6 DD ©2025 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center Accessi 8 * ∞ & 27 Λ <6 T Y U DII DD FB 8° - A 1 2 小 F10 F11 ) ) 9 0 יו 0 P {

for B in question 2, the inner product Is the picture given alone

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_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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 ]

Videos

Answer to Problem 1SE

Explanation of Solution

Answer to Problem 1SE

Explanation of Solution

Want to see more full solutions like this?

Chapter 2 Solutions

Additional Math Textbook Solutions