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00:5700:57, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 10 (b) ‎No edit summary current
00:5700:57, 2 April 2025 diff hist +386‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 10 (b)/Statement ‎No edit summary current
00:5300:53, 2 April 2025 diff hist +207‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 10 (b)/Statement ‎ Created page with "The matrix A and the vectors v1, v2 and v3 are the same as in the previous part. Let W be a 2-dimensional subspace of R 3 such that, whenever a vector x is in W, the vector Ax is also in W. Suppose a vector"
00:5200:52, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 10 (a) ‎No edit summary current
00:5200:52, 2 April 2025 diff hist +15‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 10 (a)/Statement ‎No edit summary current
00:5000:50, 2 April 2025 diff hist +503‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 10 (a)/Statement ‎ Created page with "Let <math> A </math> be a <math> 3\times 3 </math> matrix, and let <math> S=\{{\bf{v}}_1, {\bf{v}}_2, {\bf{v}}_3} </math> be a linearly independent set in <math> \mathbb{R}^3 </math> such that <math display = "block"> A{\bf{v}}_1={\bf{v}}_1, A{\bf{v}}_2=-{\bf{v}}_2, A{\bf{v}}_3={\bf{0}}. </math> Let <math> {\bf{w}}={\bf{v}}_1+{\bf{v}}_2+{\bf{v}}_3 </math>. Show that <math> {\bf{v}}_1,\;{\bf{v}}_2 </math> and <math> {\bf{v}}_3 </math> are all in <math> {\rm{Span}}\{{\b..."
00:3500:35, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (d) ‎No edit summary current
00:3500:35, 2 April 2025 diff hist +1‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (d)/Statement ‎No edit summary current
00:3500:35, 2 April 2025 diff hist +5‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (d)/Statement ‎No edit summary
00:3400:34, 2 April 2025 diff hist +315‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (d)/Statement ‎No edit summary
00:3100:31, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (c) ‎No edit summary current
00:3100:31, 2 April 2025 diff hist +155‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (d)/Statement ‎ Created page with "Suppose now that, as well as the movement between Delta and Surrey, people immigrate from elsewhere (Abbotsford). This changes the dynamical system so that"
00:3100:31, 2 April 2025 diff hist +55‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (c)/Statement ‎ Created page with "In the long run, what will the population of Surrey be?" current
00:3000:30, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (b) ‎No edit summary current
00:2900:29, 2 April 2025 diff hist +443‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (b)/Statement ‎ Created page with "Let <math> \lambda_1 </math> and <math> \lambda_2 </math> denote the two eigenvalues of the matrix A. Compute <math> \lambda_1 </math> and <math> \lambda_2 </math> and two associated eigenvectors <math> {\bf{x}}_1 </math> and <math> {\bf{x}}_2 </math>. Find some constants <math> a </math> and <math> b </math> such that: <math display = "block"> \begin{bmatrix} d_n\\s_n\end{bmatrix} = a\lambda_1^n{\bf{x}}_1+ b\lambda_2^n{\bf{x}}_2. </math>" current
00:2200:22, 2 April 2025 diff hist +8‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (a)/Statement ‎No edit summary current
00:2200:22, 2 April 2025 diff hist +161‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (a)/Statement ‎No edit summary
00:2000:20, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (a) ‎No edit summary current
00:2000:20, 2 April 2025 diff hist +74‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (a)/Statement ‎No edit summary
00:1800:18, 2 April 2025 diff hist +432‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 09 (a)/Statement ‎ Created page with "There are two cities, Delta and Surrey. Every year • 10% of the population of Delta migrates to Surrey, • 20% of the population of Surrey migrates to Delta. Assume there are no other changes to the population of Delta or Surrey. In 2019 it was estimated that the population of Delta was 100,000 people, and that of Surrey was 500,000 people. Let dn and sn respectively denote the population of Delta and Surrey n years from now."
00:1800:18, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (d) ‎No edit summary current
00:1800:18, 2 April 2025 diff hist +39‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (d)/Statement ‎ Created page with "Calculate <math> (I_3-A)^{888} </math>." current
00:1700:17, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (c) ‎No edit summary current
00:1600:16, 2 April 2025 diff hist +58‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (c)/Statement ‎ Created page with "Write down a basis for the null space of <math> A </math>." current
00:1500:15, 2 April 2025 diff hist −4‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (a)/Statement ‎No edit summary current
00:1400:14, 2 April 2025 diff hist −2‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (a)/Statement ‎No edit summary
00:1400:14, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (b) ‎No edit summary current
00:1300:13, 2 April 2025 diff hist +7‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (b)/Statement ‎No edit summary current
00:1300:13, 2 April 2025 diff hist +187‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (b)/Statement ‎ Created page with "The transformation <math> T: \mathbb{R}^3\to \mathbb{R}^3 </math> given by <math> T(x)={\rm{proj}}_W{\bf{x}} </math> is linear. Write down the matrix <math> A </math> of <math> T </math>."
00:1100:11, 2 April 2025 diff hist +23‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (a)/Statement ‎No edit summary
00:1000:10, 2 April 2025 diff hist +127‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (a)/Statement ‎No edit summary
00:0800:08, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (a) ‎No edit summary current
00:0200:02, 2 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (a)/Statement ‎No edit summary
00:0200:02, 2 April 2025 diff hist +12‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (a)/Statement ‎No edit summary
00:0100:01, 2 April 2025 diff hist +2‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (a)/Statement ‎No edit summary
00:0100:01, 2 April 2025 diff hist +296‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 08 (a)/Statement ‎ Created page with "Let <math display = "block> W=Span\left\{\begin{bmatrix} 1\\1\\1\end{bmatrix};\;\begin{bmatrix}1\\1\\-2\end{bmatrix}\right\}. </math> The following has been calculated already: <math display = "block> proj_{W}\begin{bmatrix}1\\0\\0\end{bmatrix}=\begin{bmatrix}1/2\\1/2\\0\end{bmatrix}. </math>"

23:4923:49, 1 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 07 (b) ‎No edit summary current
23:4923:49, 1 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 07 (c) ‎No edit summary current
23:4723:47, 1 April 2025 diff hist +1‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 07 (c)/Statement ‎No edit summary current
23:4523:45, 1 April 2025 diff hist +210‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 07 (c)/Statement ‎ Created page with "Consider the solution you found in the previous part. Call this vector <math> {\bf{v}} </math>. What is the distance between <math> A{\bf{v}} </math> and <math> \begin{bmatrix} 11\\0\11\\0\end{bmatrix}? </math>"
23:4023:40, 1 April 2025 diff hist +1‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 07 (b)/Statement ‎No edit summary current
23:3923:39, 1 April 2025 diff hist +260‎ N Science:Math Exam Resources/Courses/MATH221/December 2019/Question 07 (b)/Statement ‎ Created page with "The system <math display = "block"> A=\begin{bmatrix} 1& 0&1\\0&1&-1\\0&2&1\\0&-1&0\end{bmatrx},\quad {\bf{b}}=\begin{bmatrix} 11\\0\\11\\0\end{bmatrix} </math> is inconsistent. Find the least-squares solution of the system <math> A{\bf{x}}={\bf{b}}.</math>"
23:3323:33, 1 April 2025 diff hist +1‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 07 (a)/Statement ‎No edit summary current
23:3323:33, 1 April 2025 diff hist 0‎ Science:Math Exam Resources/Courses/MATH221/December 2019/Question 07 (a) ‎No edit summary current

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