IIT M DIPLOMA AN4 EXAM QDD4 25 Feb 2024 - 25 Feb 2024

MLF Quiz 111 questions40 marks6 MCQ · 4 MSQ · 1 SADiploma / QDD4

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Comprehension passage - the questions below it refer to this

Q1MCQ4 marks

Find the row space of matrix A.

Q2MCQ3 marks

Find the column space of matrix A.

Q3MCQ3 marks

Q4MCQ3 marks

Q5MCQ4 marks

Find the best fit line for the dataset given below using least squares method. question figure

Find the best fit line for the dataset given below using least squares method.

Q6MCQ4 marks

Q7MSQ3 marksselect all that apply

Which of the following is/are supervised learning task(s)?

Predicting future sales of a product based on the past sales data.
Reducing the dimensionality of images while retaining essential features,enabling efficient storage and transmission.
Recognizing and interpreting handwritten characters or words, often used indigit recognition or reading handwritten text.
Categorizing text documents into predefined classes, such as spam or non-spam emails.

Q8MSQ4 marksselect all that apply

Q9MSQ4 marksselect all that apply

Let A and B be symmetric matrices such that AB = BA. Then which of the following options is/are true?

Q10MSQ4 marksselect all that apply

Q11SA4 marks

Your numeric answer:

Answer key

Auto-generated summary from the source site. Handy as a checklist; the lessons above explain each idea from scratch.

Matrix Operations: Understanding matrix multiplication, inversion, and diagonalization.
- Diagonalization: $P^{-1}AP = D$ , where $D$ is a diagonal matrix.
Vector Spaces: Row space and column space of a matrix.
- Row Space: Span of the row vectors of a matrix.
- Column Space: Span of the column vectors of a matrix.
Eigenvalues and Eigenvectors: Understanding how to find eigenvalues and eigenvectors of a matrix.
- Eigenvalue Equation: $Av = \lambda v$ , where $A$ is a matrix, $v$ is an eigenvector, and $\lambda$ is an eigenvalue.
Symmetric Matrices: Properties of symmetric matrices and their diagonalization.
- Symmetric Matrix: $A = A^T$ .
- Orthogonal Diagonalization: $A = PDP^T$ , where $P$ is orthogonal and $D$ is diagonal.

Linear Approximation: Using the tangent line to approximate the value of a function near a point.
- Linear Approximation Formula: $f(x) \approx f(a) + f'(a)(x - a)$ .
Multivariable Calculus: Partial derivatives and directional derivatives.
- Partial Derivatives: $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$ .
- Directional Derivative: $D_{\mathbf{u}} f(a, b) = \nabla f(a, b) \cdot \mathbf{u}$ .
Limits and Continuity: Understanding the behavior of functions as they approach certain points.
- Limit Definition: $\lim_{x \to a} f(x) = L$ .
- Continuity: A function $f$ is continuous at $a$ if $\lim_{x \to a} f(x) = f(a)$ .

Supervised Learning: Tasks where the model is trained on labeled data.
- Examples: Predicting sales, recognizing handwritten characters, categorizing text documents.
Dimensionality Reduction: Techniques to reduce the number of features in a dataset.
- Encoder-Decoder Pair: Functions to reduce and reconstruct data dimensions.
- Reconstruction Error: $R(f, g) = \frac{1}{n} \sum_{i=1}^{n} \| X_i - g(f(X_i)) \|^2$ .

Best Fit Line: Finding the line that minimizes the sum of the squared differences between the observed and predicted values.
- Least Squares Formula: $y = mx + b$ , where $m$ and $b$ are chosen to minimize the sum of squared errors.