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Questions and Answers
Film scripts use descriptions of character's thoughts to detail a scene.
Film scripts use descriptions of character's thoughts to detail a scene.
False (B)
In a film script, dialogues are formatted with the character's name below their lines.
In a film script, dialogues are formatted with the character's name below their lines.
False (B)
Stage directions in a play script guide the audience's interpretation of the play.
Stage directions in a play script guide the audience's interpretation of the play.
False (B)
Dialogue in a playscript is presented without character names before each line.
Dialogue in a playscript is presented without character names before each line.
The primary purpose of a movie poster is to analyze the film's themes.
The primary purpose of a movie poster is to analyze the film's themes.
A film poster always includes extensive plot summaries to attract viewers.
A film poster always includes extensive plot summaries to attract viewers.
A comprehensive film review will only assess the technical aspects of the movie.
A comprehensive film review will only assess the technical aspects of the movie.
The conclusion of a film review typically avoids offering a final recommendation.
The conclusion of a film review typically avoids offering a final recommendation.
The purpose of an instructional text is to entertain the reader with a fictional narrative.
The purpose of an instructional text is to entertain the reader with a fictional narrative.
Instructional texts commonly feature a sequential structure, often using numbered steps or random paragraphs.
Instructional texts commonly feature a sequential structure, often using numbered steps or random paragraphs.
Flashcards
Scene Descriptions in Film Script
Scene Descriptions in Film Script
A film script includes scene descriptions detailing the setting, actions, and visual elements to help the director and crew visualize the scene.
Dialogue Formatting in Film Script
Dialogue Formatting in Film Script
In a film script, dialogues are formatted by character name followed by the spoken lines, typically indented to distinguish them from scene descriptions.
Purpose of Stage Directions
Purpose of Stage Directions
The main purpose of stage directions in a play script is to guide actors' movements, expressions, and the overall staging of the play.
Dialogue Presentation in Play Script
Dialogue Presentation in Play Script
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Primary Purpose of a Poster
Primary Purpose of a Poster
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Elements Assessed in Film Review
Elements Assessed in Film Review
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Common Theme in Fairy Tales
Common Theme in Fairy Tales
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Conclusion of a Film Review
Conclusion of a Film Review
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Purpose of Instructional Text
Purpose of Instructional Text
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Structure of Instructional Texts
Structure of Instructional Texts
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Study Notes
- A matrix $A$ is a table of real or complex numbers, known as coefficients, arranged in $n$ rows and $p$ columns.
- $A = (a_{ij}){\substack{1 \leq i \leq n \ 1 \leq j \leq p}}$ or $A = \begin{pmatrix} a{11} & a_{12} & \cdots & a_{1p} \ a_{21} & a_{22} & \cdots & a_{2p} \ \vdots & \vdots & \ddots & \vdots \ a_{n1} & a_{n2} & \cdots & a_{np} \end{pmatrix}$
- $M_{n,p}(\mathbb{K})$ denotes the set of matrices with $n$ rows and $p$ columns with coefficients in $\mathbb{K}$ ($\mathbb{K} = \mathbb{R}$ or $\mathbb{C}$).
Special Cases
- A matrix is square of order $n$ if $n = p$. $M_n(\mathbb{K})$ is written instead of $M_{n,n}(\mathbb{K})$.
- A matrix is a row matrix if $n = 1$.
- A matrix is a column matrix if $p = 1$.
Matrix Operations
- Addition: If $A, B \in M_{n,p}(\mathbb{K})$, then $A + B = (a_{ij} + b_{ij})_{\substack{1 \leq i \leq n \ 1 \leq j \leq p}}$.
- Multiplication by a scalar: If $A \in M_{n,p}(\mathbb{K})$ and $\lambda \in \mathbb{K}$, then $\lambda A = (\lambda a_{ij})_{\substack{1 \leq i \leq n \ 1 \leq j \leq p}}$.
- Matrix product: If $A \in M_{n,p}(\mathbb{K})$ and $B \in M_{p,q}(\mathbb{K})$, then $AB = C \in M_{n,q}(\mathbb{K})$ with $c_{ij} = \sum_{k=1}^p a_{ik}b_{kj}$.
- Matrix multiplication is generally non-commutative: $AB \neq BA$ in general.
Specific matrices
- Null matrix: $0 = (0)_{\substack{1 \leq i \leq n \ 1 \leq j \leq p}}$.
- Identity matrix: $I_n = (\delta_{ij}){\substack{1 \leq i \leq n \ 1 \leq j \leq n}}$ where $\delta{ij} = \begin{cases} 1 & \text{if } i = j \ 0 & \text{if } i \neq j \end{cases}$.
- Diagonal matrix: $D = (d_{ij}){\substack{1 \leq i \leq n \ 1 \leq j \leq n}}$ with $d{ij} = 0$ if $i \neq j$.
- Upper triangular matrix: $T = (t_{ij}){\substack{1 \leq i \leq n \ 1 \leq j \leq n}}$ with $t{ij} = 0$ if $i > j$.
- Lower triangular matrix: $T = (t_{ij}){\substack{1 \leq i \leq n \ 1 \leq j \leq n}}$ with $t{ij} = 0$ if $i < j$.
- Symmetric matrix: $A = (a_{ij}){\substack{1 \leq i \leq n \ 1 \leq j \leq n}}$ with $a{ij} = a_{ji}$.
- Antisymmetric matrix: $A = (a_{ij}){\substack{1 \leq i \leq n \ 1 \leq j \leq n}}$ with $a{ij} = -a_{ji}$.
Transposition
- The transpose of a matrix $A = (a_{ij}){\substack{1 \leq i \leq n \ 1 \leq j \leq p}} \in M{n,p}(\mathbb{K})$ is the matrix $A^T = (a_{ji}){\substack{1 \leq i \leq p \ 1 \leq j \leq n}} \in M{p,n}(\mathbb{K})$.
- $(A + B)^T = A^T + B^T$
- $(\lambda A)^T = \lambda A^T$
- $(AB)^T = B^T A^T$
- $(A^T)^T = A$
Inverse of a matrix
- A square matrix $A \in M_n(\mathbb{K})$ is said to be invertible if there exists a matrix $B \in M_n(\mathbb{K})$ such that $AB = BA = I_n$.
- The matrix $B$ is then called the inverse of $A$ and is denoted $A^{-1}$.
- If $A$ is invertible, then $A^{-1}$ is invertible and $(A^{-1})^{-1} = A$.
- If $A$ and $B$ are invertible, then $AB$ is invertible and $(AB)^{-1} = B^{-1} A^{-1}$.
- If $A$ is invertible, then $A^T$ is invertible and $(A^T)^{-1} = (A^{-1})^T$.
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