Solve the system by writing a matrix equation, then solve using the inverse with a calculator.
5. You have 37 coins that are nickels, dimes, and pennies. The total value of the coins is $1.55. There are twice as many pennies as dimes. Find the number of each type of coin in the bank.
Answer: Let n be the number of nickels, d be the number of dimes, and p be the number of pennies. The system is
1st equation:
2nd equation:
3rd equation:
Matrix Equation:
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The solution is pennies, dimes and
nickels.
Homework Answers
Add Answer to:
Solve the system by writing a matrix equation, then
solve using the inverse with a calculator....
Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Axequals=b. Then solve the system and write the solution as a vector. Aequals=left...
Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Axequals=b. Then solve the system and write the solution as a vector. Aequals=left bracket Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column 3 3rd Column negative 2 2nd Row 1st Column negative 2 2nd Column negative 2 3rd Column 0 3rd Row 1st Column 5 2nd Column 2 3rd Column 6 EndMatrix right bracket 1...
2. Solve the following linear systems of equations by writing the system as a matrix equation...
2. Solve the following linear systems of equations by writing the system as a matrix equation Ax = b and using the inverse of the matrix A. (You may use a calculator or computer software to find A-1. Or you can find A-1 by row-reduction.) 3x1 – 2x2 + 4x3 = 1 x1 + x2 – 2x3 = 3 2x1 + x2 + x3 = 8 321 – 2x2 + 4x3 = 10 X1 + x2 – 2x3 = 30...
3 (b) Write the following systems of linear equations as matrix equation and then as an...
3 (b) Write the following systems of linear equations as matrix
equation and then as an augmented matrix:
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(d) Use Cramer’s rule to solve the system of 2 linear equations
in 3(b). (7marks)
We were unable to transcribe this imageWe were unable to transcribe this image
If the given matrix is invertible, find its inverse. A = a.) A-1 = We were...
If the given matrix is invertible, find its inverse.
A =
a.) A-1 =
We were unable to transcribe this imageWe were unable to transcribe this image
Solve the system using the inverse of a 2 x 2 matrix. – 7x + 6y...
Solve the system using the inverse of a 2 x 2 matrix. – 7x + 6y = 31 63 – 5y = -26 a. With X = , the matrix equation, AX= B, corresponding to this system is: LU X = b. The inverse of the coefficient matrix is: A-1 = | c. The solution to the matrix equation is: X= A-1B= |
Solve the following system of linear equations by hand by writing an equivalent matrix equation and...
Solve the following system of linear equations by hand by writing an equivalent matrix equation and using matrix algebra: -x1+x2=3 2x1-3x2=-2
Let and solve the first equation for as a function of and c. u2 (At)2...
Let and solve the first equation for as a function of and c. u2 (At)2 2 We were unable to transcribe this image2D We were unable to transcribe this imageWe were unable to transcribe this image
Please help solve this, using the equation to get through the problem. Additional information: where the...
Please help solve this, using the equation
to get through the problem.
Additional information:
where the initial position
, the initial speed
The above differential equation can also be written as:
If
, there is light damping where the solution has the form ( where r
and w are two positive constants)
or
If
there is heavy damping where,
where
and
are two positive constants
If
there is critical damping where,
where r is a positive constant
d'y dy ma...
Consider the following non-homogeneous system of differential equations. a. Write the system in matrix form. b....
Consider the following non-homogeneous system of differential
equations.
a. Write the system in matrix form.
b. Find the homogeneous solution.
c. Find the particular solution.
d. Write down the general solution.
We were unable to transcribe this imageWe were unable to transcribe this image
Solve the linear system using an inverse matrix. -4x +5y 12 The inverse of the coefficient...
Solve the linear system using an inverse matrix. -4x +5y 12 The inverse of the coefficient matrix A, A 1 is (Simplify your answer. Type an integer or simplified fraction for each matrix element) The solution to the system is x-and y Simplify your answers. Type integers or simplified fractions) Enter your answer in each of the answer boxes
2. Solve the following linear systems of equations by writing the system as a matrix equation Ax = b and using the inverse of the matrix A. (You may use a calculator or computer software to find A-1. Or you can find A-1 by row-reduction.) 3x1 – 2x2 + 4x3 = 1 x1 + x2 – 2x3 = 3 2x1 + x2 + x3 = 8 321 – 2x2 + 4x3 = 10 X1 + x2 – 2x3 = 30...
3 (b) Write the following systems of linear equations as matrix
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(d) Use Cramer’s rule to solve the system of 2 linear equations
in 3(b). (7marks)
We were unable to transcribe this imageWe were unable to transcribe this image
If the given matrix is invertible, find its inverse.
A =
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We were unable to transcribe this imageWe were unable to transcribe this image
Solve the system using the inverse of a 2 x 2 matrix. – 7x + 6y = 31 63 – 5y = -26 a. With X = , the matrix equation, AX= B, corresponding to this system is: LU X = b. The inverse of the coefficient matrix is: A-1 = | c. The solution to the matrix equation is: X= A-1B= |
Please help solve this, using the equation
to get through the problem.
Additional information:
where the initial position
, the initial speed
The above differential equation can also be written as:
If
, there is light damping where the solution has the form ( where r
and w are two positive constants)
or
If
there is heavy damping where,
where
and
are two positive constants
If
there is critical damping where,
where r is a positive constant
d'y dy ma...
Consider the following non-homogeneous system of differential
equations.
a. Write the system in matrix form.
b. Find the homogeneous solution.
c. Find the particular solution.
d. Write down the general solution.
We were unable to transcribe this imageWe were unable to transcribe this image
Solve the linear system using an inverse matrix. -4x +5y 12 The inverse of the coefficient matrix A, A 1 is (Simplify your answer. Type an integer or simplified fraction for each matrix element) The solution to the system is x-and y Simplify your answers. Type integers or simplified fractions) Enter your answer in each of the answer boxes
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