The system of equations in matrix form is written:

Beginning with the top equation, insert each coefficient into the top row of the matrix, from left to right. Then, place the 2 on the right hand side of the vertical line (anytime you see this vertical line in a matrix, it is called an augmented matrix. Because the first equation's coefficients are 1, 1, and 1, these form the top row of the matrix, with 2 on the right side of the bar. Then, move on to the second row, which has coefficients 2, -1, and 3. Place these into the second row of the matrix, with -7 on the right hand side of the vertical bar. Finally, take the coefficients from the 3rd equation, 1, 1, and -1, and place these in the bottom row with 6 on the right hand side of the vertical bar.

The system of equations in matrix form is written:

Beginning with the top equation, insert each coefficient into the top row of the matrix, from left to right. Then, place the 2 on the right hand side of the vertical line (anytime you see this vertical line in a matrix, it is called an augmented matrix. Because the first equation's coefficients are 1, 1, and 1, these form the top row of the matrix, with 2 on the right side of the bar. Then, move on to the second row, which has coefficients 2, -1, and 3. Place these into the second row of the matrix, with -7 on the right hand side of the vertical bar. Finally, take the coefficients from the 3rd equation, 1, 1, and -1, and place these in the bottom row with 6 on the right hand side of the vertical bar.

For two matrices to be equal, two conditions must hold:

1. The matrices must have the same dimension. This can be seen to be the case, since both matrices have two rows and one column.

2. All corresponding entries must be equal. For this to happen, it must hold that

This is a system of two equations in two variables, which can be solved as follows:

Add both sides of the equations:

It follows that

Substitute back:

Thus, there exists a solution to the system, and, consequently, to the original matrix equation. The statement is therefore false.

For two matrices to be equal, two conditions must hold:

1. The matrices must have the same dimension. This can be seen to be the case, since both matrices have two rows and one column.

2. All corresponding entries must be equal. For this to happen, it must hold that

This is a system of two equations in two variables, which can be solved as follows:

Add both sides of the equations:

It follows that

Substitute back:

Thus, there exists a solution to the system, and, consequently, to the original matrix equation. The statement is therefore false.

Arrange the equations into the form:

, where a,b,c,d are constants.

Then we have the system of equations: .

The augmented matrix is found by copying the constants into the respective rows and columns of a matrix.

The vertical line in the matrix is analogous to the = sign thus resulting in the following:

First, it must be established that is defined. This is the case if and only and have the same number of rows, which is true, and they have the same number of columns, which is also true. is therefore defined.

Addition of two matrices is performed by adding corresponding elements, so

This is the two-by-two identity . Therefore, .

Arrange the equations into the form:

, where a,b,c,d are constants.

Then we have the system of equations: .

The augmented matrix is found by copying the constants into the respective rows and columns of a matrix.

The vertical line in the matrix is analogous to the = sign thus resulting in the following:

First, it must be established that is defined. This is the case if and only and have the same number of rows, which is true, and they have the same number of columns, which is also true. is therefore defined.

Addition of two matrices is performed by adding corresponding elements, so

This is the two-by-two identity . Therefore, .

The system of equations in matrix form is written:

The system of equations in matrix form is written: