| Square Matrices and Identity Matrices |
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| 1) Which of the following matrices are square matrices? Explain. |
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| 2) Which of the following is an identity matrix? |
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| 3) Write the solution as a matrix. Just type the answer, by rows, without the matrix symbols. |
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4) True or False? Matrices F and G are inverses of each other. Explain why.
Hint: Multiply the matrices (F × G and G × F) to see if their products produce the identity matrix (I). |
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5) True or False? Matrices L and M are inverses of each other. Explain why.
Hint: Does L × M = I? Does M × L = I? |
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6) Calculate the determinant to determine if the matrix has an inverse.
(a) State the determinant.
(b) If the matrix has an inverse, state true; if not, state false. |
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7) Calculate the determinant to determine if the matrix has an inverse.
(a) State the determinant.
(b) If the matrix has an inverse, state true; if not, state false. |
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| In the following problems, find the inverse matrix, if it exists. If the inverse does not exist, write “no inverse”. If the inverse does exist, just type the answer, by rows, without the matrix symbols. |
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| 8) Find the inverse matrix, if it exists. |
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| 9) Find the inverse matrix, if it exists. |
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| Solving Systems with Matrix Equations |
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| 10) State the matrix equation that represents this system. Just type the answer, by rows, without the matrix symbols for the coefficient matrix, the variable matrix, and the constant matrix. |
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| 11) State the system of equations represented by this matrix equation. |
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| Use the given system of equations to answer the following questions. |
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| 12) State the matrix equation that represents this system. Just type the answer, by rows, without the matrix symbols for the coefficient matrix, the variable matrix, and the constant matrix. |
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| 13) Find the inverse of the coefficient matrix. Just type the answer, by rows, without the matrix symbols. |
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15) Find the difference. State the letter of the correct answer.
Hint: Subtract the entries that have the same address in each matrix.
Click here to review the unit content explanation for Matrices. |
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16) Find the product of “f” and “g”.
Click here to review the unit content explanation for Functions and Inverses of Functions. |
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18) Perform the composition for the given functions.
Recall: When composing functions, substitute the expression of one function in for x in the other function as directed by the given composition.
Click here to review the unit content explanation for Functions and Inverses of Functions. |
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19) Which equation contains the points (1, –4) and (–3, 4)?
Hint: There are a variety of ways to solve this problem; however, finding the slope and using the point-slope formula will give the desired equation.
Click here to review the unit content explanation for Linear Equations. |
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| 20) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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