Introduction to Matrices
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Introduction to Matrices
7 problems
1PRACTICE PROBLEM
Perform the following matrix operation: 9A
2PRACTICE PROBLEM
Find the given matrices (if possible):
a. PQ
b. QP
3PRACTICE PROBLEM
Apply the indicated row transformation to the following matrix.
![{"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced open=\"[\" close=\"]\"><mtable><mtr><mtd><mn>6</mn></mtd><mtd><mo>-</mo><mn>9</mn></mtd></mtr><mtr><mtd><mn>11</mn></mtd><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></mstyle></math>","truncated":false}](https://lightcat-files.s3.amazonaws.com/problem_images/ea00f04ac199ccc6-1682504368285.jpg "open square brackets table row 6 cell negative 9 end cell row 11 0 end table close square brackets"){kind=small}
Add the result -10 times of row 1 to row 2
4PRACTICE PROBLEM
What is the system of equations associated with the following augmented matrix? Please note that you don't need to solve it.
![{"mathml":"<math style=\"font-family:stix;font-size:16px;\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathsize=\"16px\"><mfenced open=\"[\" close=\"]\"><mrow><mtable><mtr><mtd><mn>4</mn></mtd><mtd><mn>7</mn></mtd><mtd><mn>5</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mn>7</mn></mtd><mtd><mn>6</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>5</mn></mtd><mtd><mo>-</mo><mn>7</mn></mtd><mtd><mn>4</mn></mtd></mtr></mtable><menclose notation=\"left\"><mtable><mtr><mtd><mn>3</mn></mtd></mtr><mtr><mtd><mn>19</mn></mtd></mtr><mtr><mtd><mn>31</mn></mtd></mtr></mtable></menclose></mrow></mfenced></mstyle></math>","truncated":false}](https://lightcat-files.s3.amazonaws.com/problem_images/39735bf33130a4a9-1682506072278.jpg "open square brackets table row 4 7 5 row 3 7 6 row cell negative 5 end cell cell negative 7 end cell 4 end table left enclose table row 3 row 19 row 31 end table end enclose close square brackets")
5PRACTICE PROBLEM
Using Gaussian elimination with back-substitution or Gauss-Jordan elimination, solve the given system of equations.
7PRACTICE PROBLEM
For the following system of equations, use the Gaussian elimination method to determine the solution or to identify if no solution exists:
