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Questions and Answers
What is the result of performing the operation $R_1 \to 4R_1$ on the matrix $A = \begin{bmatrix} 2 & 0 \ 3 & 4 \end{bmatrix}$?
What is the result of performing the operation $R_1 \to 4R_1$ on the matrix $A = \begin{bmatrix} 2 & 0 \ 3 & 4 \end{bmatrix}$?
- \begin{bmatrix} 2 & 0 \\ 12 & 4 \end{bmatrix}
- \begin{bmatrix} 4 & 0 \\ 3 & 4 \end{bmatrix}
- \begin{bmatrix} 0 & 2 \\ 3 & 4 \end{bmatrix}
- \begin{bmatrix} 8 & 0 \\ 3 & 4 \end{bmatrix} (correct)
If the operation $C_2 \to -3C_2$ is performed on $A = \begin{bmatrix} 2 & 0 \ 3 & 4 \end{bmatrix}$, what is the resulting matrix?
If the operation $C_2 \to -3C_2$ is performed on $A = \begin{bmatrix} 2 & 0 \ 3 & 4 \end{bmatrix}$, what is the resulting matrix?
- \begin{bmatrix} 2 & 0 \\ -9 & 4 \end{bmatrix}
- \begin{bmatrix} 2 & -12 \\ 3 & 4 \end{bmatrix}
- \begin{bmatrix} 2 & 0 \\ 3 & -12 \end{bmatrix} (correct)
- \begin{bmatrix} 0 & -12 \\ 3 & 4 \end{bmatrix}
What does the operation $R_i \to R_i + kR_j$ accomplish?
What does the operation $R_i \to R_i + kR_j$ accomplish?
- It multiplies row $R_i$ by a constant.
- It swaps row $R_i$ with row $R_j$.
- It replaces row $R_i$ with the sum of rows $R_i$ and $R_j$.
- It adds multiples of row $R_j$ to row $R_i$. (correct)
Which operation modifies a specific column of the matrix?
Which operation modifies a specific column of the matrix?
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What will be the result of the operation $C_i \to C_i + kC_j$?
What will be the result of the operation $C_i \to C_i + kC_j$?
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Study Notes
Row Operations
- Multiplying a row by a constant:
- $R_i \to kR_i$
- Multiply each element in row $R_i$ by the constant $k$.
- Adding a multiple of a row to another row:
- $R_i \to R_i + kR_j$
- Multiply each element in row $R_j$ by the constant $k$ and add the result to the corresponding element in row $R_i$.
Column Operations
- Multiplying a column by a constant:
- $C_j \to kC_j$
- Multiply each element in column $C_j$ by constant $k$.
- Adding a multiple of a column to another column:
- $C_i \to C_i + kC_j$
- Multiply each element in column $C_j$ by the constant $k$ and add the result to the corresponding element in column $C_i$.
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