Solving Linear Systems with Matrix Inverses

Solving Systems with Inverse Matrices

​Another example:

Multiple Choice

Which numbers are correct for the first row in the coefficient matrix?

• $$\left[5\ \ 0\ \ -10\right]$$

• $$\left[2\ \ 3\ \ -1\right]$$

• $$\left[-6\ \ 1\ \ -4\right]$$

• $$\left[5\ \ 0\ \ 0\right]$$

Multiple Choice

Which numbers are correct for the 2nd row in the coefficient matrix?

• $$\left[2\ \ 3\ \ 0\right]$$

• $$\left[2\ \ 3\ \ -1\right]$$

• $$\left[-6\ \ 1\ \ -4\right]$$

• $$\left[5\ \ 0\ \ 0\right]$$

Multiple Choice

Which numbers are correct for the 3rd row in the coefficient matrix?

• $$\left[2\ \ 3\ \ 0\right]$$

• $$\left[-6\ \ 1\ \ 4\right]$$

• $$\left[-6\ \ 1\ \ -4\right]$$

• $$\left[-6\ \ 0\ \ 4\right]$$

Multiple Choice

Which numbers are correct for the constant matrix?

• -10

  -1

  -11

• -10 -1 -11

• 10

  1

  11

• 10 1 11

Multiple Choice

When solving system using the inverse, which two matrices do you multiply?

• coefficient matrix is multiplied by the constant matrix

• the inverse of the coefficient matrix is multiplied by the constant matrix

• coefficient matrix is multiplied by the solution matrix

• the inverse of the coefficient matrix is multiplied by the solution matrix

Multiple Choice

Solve for x, y and z.

• (2, 1, 6)
• (1, -2, 6)
• (6, 1, 2)
• (-2, 1, 6)

Multiple Choice

Solve the system of linear equations using the inverse matrix.

• (3, 1, -5)

• (-3, 1, -1)

• not possible; the inverse does not exist

Multiple Select

What two keystrokes will pull up the box for you to type in the dimensions of the matrix?

• 2nd

• x^-1

• alpha

• zoom

Multiple Choice

What are the numbers in the first row of the coefficient matrix?

• $$\left[1\ \ 1\ \ 1\ \ -3\right]$$

• $$\left[1\ \ -1\ \ 1\right]$$

• $$\left[1\ \ -1\ \ 1\ \ -3\right]$$

• $$\left[1\ \ 1\ \ 1\right]$$

Multiple Choice

What are the numbers in the second row of the coefficient matrix?

• $$\left[1\ \ -1\ \ -1\ \ 3\right]$$

• $$\left[1\ \ -1\ \ -1\right]$$

• $$\left[1\ \ 1\ \ 1\right]$$

• $$\left[-3\ \ 1\ \ 1\right]$$

Multiple Choice

What are the numbers in the 3rd row of the coefficient matrix?

• $$\left[5\ \ 5\ \ 1\right]$$

• $$\left[5\ \ -5\ \ 1\right]$$

• $$\left[5\ \ 5\ \ 0\ \ -15\right]$$

• $$\left[5\ \ 5\ \ 1\ \ 15\right]$$

Multiple Choice

Solve the system:

-4x - 5y - z = 18

-2x - 5y - 2z = 12

-2x + 5y + 2z = 4

• (4, 0, -2)
• (-4, 0, -2)
• Many Solutions
• No Solution

Multiple Choice

Solve the system of equations:

5x - 4y +z = -18

x +3y +7z = 38

4x + 2y - 6z = -38    

 

• (-3,2,5)
• (3,2,5)

• Does not exist.

• (5,-4,1)

Multiple Choice

Solve:

-3x + 3y + 6z = 4

3x + y + 2z = 3

-6x + 2y + 4z = 34

• (5,-7/3,0)
  

• No Solution

• Infinite Solution

• (-5,7/3,0)