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Questions and Answers
What is the resulting matrix when calculating $(A - 2I)^2 + 5A$ for the matrix $A = \begin{pmatrix} 23 & 0 \ 4 & 0 \end{pmatrix}$?
What is the resulting matrix when calculating $(A - 2I)^2 + 5A$ for the matrix $A = \begin{pmatrix} 23 & 0 \ 4 & 0 \end{pmatrix}$?
- $\begin{pmatrix} 27 & 0 \ 4 & 0 \end{pmatrix}$
- $\begin{pmatrix} 29 & 0 \ 4 & 0 \end{pmatrix}$ (correct)
- $\begin{pmatrix} 30 & 0 \ 4 & 0 \end{pmatrix}$
- $\begin{pmatrix} 25 & 0 \ 4 & 0 \end{pmatrix}$
For the matrix $A = \begin{pmatrix} 42 & 1 \ 5 & 0 \end{pmatrix}$, what are the Eigen values?
For the matrix $A = \begin{pmatrix} 42 & 1 \ 5 & 0 \end{pmatrix}$, what are the Eigen values?
- 4 and 8
- 3 and 7
- 2 and 5 (correct)
- 1 and 6
How many 1 mg tablets are needed to create 20 tablets with a dosage of 3.8 mg/tablet from the options 1 mg, 3 mg, and 5 mg?
How many 1 mg tablets are needed to create 20 tablets with a dosage of 3.8 mg/tablet from the options 1 mg, 3 mg, and 5 mg?
- 5 1 mg, 10 3 mg, 5 5 mg
- 10 1 mg, 5 3 mg, 5 5 mg (correct)
- 8 1 mg, 8 3 mg, 4 5 mg
- 7 1 mg, 7 3 mg, 6 5 mg
For the matrix $A = \begin{pmatrix} 31 & 1 \ 26 & 0 \end{pmatrix}$, what is one of the corresponding Eigen vectors?
For the matrix $A = \begin{pmatrix} 31 & 1 \ 26 & 0 \end{pmatrix}$, what is one of the corresponding Eigen vectors?
To produce 25 tablets with a dosage of 4.2 mg/tablet using 2 mg, 4 mg, and 6 mg tablets, how many 4 mg tablets should be used if 10 tablets are to be of 6 mg?
To produce 25 tablets with a dosage of 4.2 mg/tablet using 2 mg, 4 mg, and 6 mg tablets, how many 4 mg tablets should be used if 10 tablets are to be of 6 mg?
Flashcards
Matrix Calculation
Matrix Calculation
Finding the value of an expression involving a matrix (example: (A - 2I)^2 + 5A).
Eigenvalue and Eigenvector
Eigenvalue and Eigenvector
The values and vectors associated with a matrix that satisfy a specific equation.
Tablet Dosage Mixing
Tablet Dosage Mixing
Combining tablets of different strengths to achieve a specific total dosage and the total number of tablets.
Matrix A
Matrix A
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2x2 Matrix
2x2 Matrix
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Study Notes
Math (101) Biotechnology Midterm Exam - Study Notes
- Question Types: Three questions on each exam. Questions involve matrix operations, eigenvalue/eigenvector calculations, and systems of equations.
- Question 1 (Matrix Operations): Find (A - 2I)² + 5A. Matrices (A) are presented in each test.
- Matrix A values: Vary for each test. Key details of each matrix (e.g., dimensions, entries) are essential for the calculation.
- Question 2 (Eigenvalues and Eigenvectors): Find the eigenvalue and eigenvector for the matrix provided.
- Matrices Vary: Use the same Matrix A values from Question 1 in each question set.
- Question 3 (Systems of Equations): A medicine comes in different dosage forms. Find the combinations to make a target dosage.
- Dosage Forms: The dosage strength (mg/tablet) varies for each test. The target number of tablets and total dosage also vary for each question
- All possible solutions: Find all valid combinations of dosages to reach the target amount.
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