1 Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for a
2
4
7
3
2 Solve the set of linear equations by Guassian elimination method : a+2b+3c=5, 3a-b+2c=8, 4a-6b-4c=-2. Find a
1
4
5
-1
3 Solve the set of linear equations by Guassian elimination method : a+2b+3c=5, 3a-b+2c=8, 4a-6b-4c=-2. Find b
4
-5
-3
5
4 Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for b
9
-3
5
-4
5 Solve the set of linear equations by Guassian elimination method : a+2b+3c=5, 3a-b+2c=8, 4a-6b-4c=-2. Find c
4
5
9
10
6 If A.x=
{-2,1,0}
{3,5,2}
{1,0,0}
{2,1,4}
7 Solve the set of linear equations by the matrix method : a+3b+2c=3 , 2a-b-3c= -8, 5a+2b+c=9. Sove for c
3
1
5
7
8 If A.x=
{2,3,0}
{2,1,0}
{-2,1,1}
{3,2,6}
9 If A.x=
{0,1,0}
{3,0,2}
{2,0,1}
{0,1,1}
10 What is a set of real or complex numbers or elements arranged in rows or columns to form a rectangular array.
set
matrix
determinant
real numbers
I don't know it
What is the answer of queation 5
1. To solve the set of linear equations by the matrix method:
Step 1: Write the coefficients of the variables and the constants in matrix form.
You have the following system of equations:
a + 3b + 2c = 3
2a - b - 3c = -8
5a + 2b + c = 9
The coefficient matrix, let's call it A, is:
A = [1 3 2; 2 -1 -3; 5 2 1]
The constant matrix, let's call it B, is:
B = [3; -8; 9]
Step 2: Calculate the inverse of matrix A.
We need the inverse of matrix A, denoted as A^-1. Use any method to find the inverse. Let's assume A^-1 = [d e f; g h i; j k l]
Step 3: Calculate the solution matrix X.
The solution matrix X is given by X = A^-1 * B, where * represents matrix multiplication.
So, we have X = A^-1 * B = [d e f; g h i; j k l] * [3; -8; 9]
The value of a is given by the element in the first row and first column of X, so a = d.
Similarly, the values of b and c can be obtained from the corresponding elements in X.
2. To solve the set of linear equations by Gaussian elimination method:
Step 1: Write the system of equations in matrix form.
You have the following system of equations:
a + 2b + 3c = 5
3a - b + 2c = 8
4a - 6b - 4c = -2
The coefficient matrix, A, is:
A = [1 2 3; 3 -1 2; 4 -6 -4]
The constant matrix, B, is:
B = [5; 8; -2]
Step 2: Perform Gaussian elimination to transform the augmented matrix [A|B] into row-echelon form.
Perform row operations to eliminate variables below the leading ones. The goal is to have zeros below the leading ones.
Step 3: Solve for the variables by back substitution.
Start from the bottom row and solve for the variable in that row using the equation formed. Substitute the value of the variable into the previous row's equation and continue solving for the variables until you obtain the values of all the variables.
The value of a can be obtained from the first row, the value of b from the second row, and the value of c from the third row.
3. To solve for b using the matrix method:
Follow the same steps as in the first question for solving for a using the matrix method. To solve for b, look at the element in the second row and first column of the solution matrix X obtained in step 3.
4. To solve for b using Gaussian elimination method:
Follow the same steps as in the second question for solving for a using Gaussian elimination method. To solve for b, look at the second row and the equation after the elimination step. The coefficient of b will be multiplied by the value of c, and the coefficient of c will be multiplied by the value of b. The resulting equation will give you the value of b.
5. To solve for c using Gaussian elimination method:
Follow the same steps as in the second question for solving for a using Gaussian elimination method. To solve for c, look at the third row and the equation after the elimination step. The coefficient of c will be multiplied by the value of b, and the coefficient of b will be multiplied by the value of c. The resulting equation will give you the value of c.
6. If A.x =
To find the value of x, you need to calculate the inverse of matrix A and multiply it by the matrix on the right-hand side. The resulting matrix will give you the values of the variables.
7. To solve for c using the matrix method:
Follow the same steps as in the first question for solving for a using the matrix method. To solve for c, look at the element in the third row and first column of the solution matrix X obtained in step 3.
8. If A.x =
To find the value of x, you need to calculate the inverse of matrix A and multiply it by the matrix on the right-hand side. The resulting matrix will give you the values of the variables.
9. If A.x =
To find the value of x, you need to calculate the inverse of matrix A and multiply it by the matrix on the right-hand side. The resulting matrix will give you the values of the variables.
10. The correct answer is matrix. A set of real or complex numbers or elements arranged in rows or columns to form a rectangular array is called a matrix. Matrices are fundamental mathematical objects used in various fields, including linear algebra, physics, computer science, and economics.