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Recent questions tagged goclasses-da-course

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Linear regression | machine learning | Gate Da |
   
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Go Classes Linear Algebra DA
Construct a matrix A with each of the following properties, or explain why no such matrix exists:(a) The column space of A contains the vector (0, 2, 1),and the null spac...
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14 14 votes
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GO Classes | DA Course| Linear Algebra
Say that $S: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3}$ and $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{4}$ are linear transformations. Which of the following must be true...
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5 5 votes
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779
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GO Classes | DA Course| Linear Algebra
Let $T: \mathbf{R}^{n} \rightarrow \mathbf{R}^{m}$ be a linear transformation with matrix $A$.How many rows and columns does $A$ have?If $x$ is in $\mathrm{R}^{n}$, then ...
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654
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GO Classes | DA Course| Linear Algebra
Circle $\mathbf{T}$ if the statement is always true, and circle $\mathbf{F}$ otherwise.A. $\mathbf{T} \quad \mathbf{F} \quad$ If $T: \mathbf{R}^{n} \rightarrow \mathbf{R}...
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7 7 votes
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848
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GO Classes | DA Course| Linear Algebra
Consider $T: \mathbf{R}^{3} \rightarrow \mathbf{R}^{4}$ given by$$T(x, y, z)=(x, x+z, 3 x-4 y+z, x) .$$Is $T$ one-to-one? Justify your answer.
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6 6 votes
2 2 answers
568
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GO Classes | DA Course| Linear Algebra
Which of the following statements are true?The transformation $T(x, y, z)=(y-1,4 x+z, x)$ is an onto linear transformation.Let $A$ be a $3 \times 4$ matrix. Then, the tra...
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6 6 votes
2 2 answers
542
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GO Classes | DA Course| Linear Algebra
Which of the following is not a condition for a transformation $T: \mathbf{R}^{n} \rightarrow \mathbf{R}^{m}$ with standard matrix $A$ to be onto?The columns of $A$ span ...
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4 4 votes
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GO Classes | DA Course| Linear Algebra
If $T: \mathbf{R}^{n} \rightarrow \mathbf{R}^{m}$ is onto, what can we say about the relative sizes of $n$ and $m$ ?
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4 4 votes
4 4 answers
653
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GO Classes | DA Course| Linear Algebra
Let $T: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}$ be the matrix mapping with corresponding matrix$$\mathbf{A}=\left[\begin{array}{ccc}1 & 2 & -1 \\-3 & -4 & 2 \\5 & 2 & ...
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529
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GO Classes | DA Course| Linear Algebra
Let $\mathrm{T}_{\mathrm{A}}: \mathbb{R}^{4} \rightarrow \mathbb{R}^{3}$ be the matrix mapping with corresponding matrix$$\mathbf{A}=\left[\begin{array}{cccc}1 & 2 & -1 &...
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GO Classes | DA Course| Linear Algebra
If $\mathrm{T}_{\mathbf{A}}: \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}$ is a matrix mapping corresponding to $\mathbf{A} \in M_{m \times n}$ and $n<m$ then $T_A$ cannot b...
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5 5 votes
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802
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GO Classes | DA Course| Linear Algebra
A vector mapping $\mathrm{T}: \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}$ is said to be onto if for each $\mathbf{b} \in \mathbb{R}^{m}$ there is at least one $\mathbf{x} ...
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10 10 votes
2 2 answers
452
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GO Classes | DA Course| Linear Algebra
Let $T: \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}$ be a linear transformation and let $A$ be the standard matrix for $T$. Then:a. $T$ maps $\mathbb{R}^{n}$ onto $\mathbb{...
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8 8 votes
2 2 answers
496
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GO Classes | DA Course| Linear Algebra
I.A vector mapping $\mathrm{T}: \mathbb{R}^{n} \rightarrow \mathbb{R}^{m}$ is said to be one-to-one if for each $\mathbf{b} \in \operatorname{Range}(\mathrm{T})$ there ex...
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5 5 votes
2 2 answers
590
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GO Classes | DA Course| Linear Algebra
Let $\mathrm{T}_{\mathrm{A}}: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3}$ be the matrix mapping with corresponding matrix$$\mathbf{A}=\left[\begin{array}{cc}1 & 4 \\-3 & 2...
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6 6 votes
2 2 answers
447
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GO Classes | DA Course| Linear Algebra
Suppose $T: \mathbf{R}^{3} \rightarrow \mathbf{R}^{3}$ is a linear transformation whose range is a plane, and suppose$$T\left(\begin{array}{l}0 \\1 \\0\end{array}\right)=...
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4 4 votes
1 1 answer
394
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GO Classes | DA Course| Linear Algebra
Let $\mathrm{T}_{\mathrm{A}}: \mathbb{R}^{4} \rightarrow \mathbb{R}^{3}$ be the matrix mapping with matrix$$\mathbf{A}=\left[\begin{array}{cccc}3 & -2 & 6 & 4 \\-1 & 0 & ...
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4 4 votes
1 1 answer
350
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GO Classes | DA Course| Linear Algebra
Let $\mathrm{T}_{\mathrm{A}}: \mathbb{R}^{2} \rightarrow \mathbb{R}^{3}$ be the matrix mapping with matrix$$\mathbf{A}=\left[\begin{array}{cc}1 & 0 \\3 & -1 \\2 & 0\end{a...
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6 6 votes
1 1 answer
526
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GO Classes | DA Course| Linear Algebra
Let $T: \mathbf{R}^{\mathbf{2}} \rightarrow \mathbf{R}^{2}$ be the linear transformation satisfying$$T\binom{1}{0}=\binom{1}{2} \quad \text { and } \quad T\binom{1}{1}=\b...
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1 1 answer
466
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Go Classes | DA Course | Machine Learning
Compute the Linear Discriminant projection for the following twodimensional dataset.- Samples for class $\omega_1: \mathbf{X}_1=\left(\mathrm{x}_1, \mathbf{x}_2\right)=\{...
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2 2 votes
1 1 answer
382
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Go Classes | DA Course | Machine Learning
Which of the following are true about two-class Gaussiam discriminant analysis? Assume you have estimated the parameters $\hat{\mu}_{\mathrm{C}}, \hat{\Sigma}_{\mathrm{C}...
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221
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Go Classes | DA Course | Machine Learning
Which statements are true of Gaussian discriminant analysis for two-class classification, specifically quadratic discrimimemt analysis (QDA) and linear discriminant analy...
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2 2 answers
395
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Go Classes | DA Course | Machine Learning
You want to train a dog identifier with Gaussian discriminant analysis. Your classifier takes an image vector as its input and outputs 1 if it thinks it is a dog, and 0 o...
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237
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Go Classes | DA Course | Machine Learning
Which one of the following statements on initialization is false?The variances of layer outputs remain unchanged during training when Xavier initialization is used.Initia...
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1 1 answer
243
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Go Classes | DA Course | Machine Learning
Which of the options are correct, select all that apply ?Maximum value of local gradient when sigmoid is used as an activation function is 0.5.Minimum value of local grad...
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1 1 answer
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Go Classes | DA Course | Machine Learning
Which of the options are correct, select all that apply?You are solving a binary classification task, and the final two layers in your network are a ReLU activation follo...
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228
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Go Classes | DA Course | Machine Learning
A NEural nnetwork has many layers, with the final two being $X$(with 4 nodes) and $Y$(with one node). Four weights $\{ w_1 = 0.1, w_2 = -0.5, w_3 = 0.8, w_4 = 0.6\}$. Con...
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204
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Go Classes | DA Course | Machine Learning
Consider the neural network below. Note that:$x$, a scalar, is the input. $a_4$, also a scalar, is the output.Each $a_i$, value is the final output for neuron $i$ in the ...
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Go Classes | DA Course | Machine Learning
Below is a neural network with weights $a,b,c, d,e, f$. The inputs are $x_1$ and $x_2$. The first hidden layer computes $r_1 = max(c \cdot x_1 + e \cdot x_2, 0)$ and $r_2...
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