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a) Write down a system of linear equations to describe the above problem. Hence, form a matrix equation, AX = B. b) Find A and the cofactor of matrix A. Hence obtain the adjoint of A. c) By using (b), find the inverse of matrix A.

a) Write down a system of linear equations to describe the above problem. Hence, form a matrix equation, AX = B. b) Find A and the cofactor of matrix A. Hence obtain the adjoint of A. c) By using (b), find the inverse of matrix A.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.3: Solving Problems With Two Variables
Problem 6OE
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This is a long question about matrices. Solve the question a, b and c for me and provide me with the full solutions. This question is about matrices. Thanks :)
3. Remy has a dairy farm with 1000 cattle. There are 100 more female cows than male cows. In 2023, there were a reduction of 20 cows overall but the population of male and female cows had risen by 2% and 3% respectively. On the same year, there were a 4% reduction in offspring populations. Given that x is the number of male cows, y is the number of female cows and z is the number of offspring. a) Write down a system of linear equations to describe the above problem. Hence, form a matrix equation, AX = B. b) Find A and the cofactor of matrix A. Hence obtain the adjoint of A. c) By using (b), find the inverse of matrix A. d) Hence, determine how many of each type of cows available at the dairy farm.
Transcribed Image Text:3. Remy has a dairy farm with 1000 cattle. There are 100 more female cows than male cows. In 2023, there were a reduction of 20 cows overall but the population of male and female cows had risen by 2% and 3% respectively. On the same year, there were a 4% reduction in offspring populations. Given that x is the number of male cows, y is the number of female cows and z is the number of offspring. a) Write down a system of linear equations to describe the above problem. Hence, form a matrix equation, AX = B. b) Find A and the cofactor of matrix A. Hence obtain the adjoint of A. c) By using (b), find the inverse of matrix A. d) Hence, determine how many of each type of cows available at the dairy farm.
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