Algebra question and answers for August 12, 2023
- Q Let A 3 4 1 2 5 3 and b Define a transformation T by T x Ax If possible find a vector x whose image under T is b...
- Q Problem 7 7 points et W x y z R 3x 2y z 0 Determine an orthonormal basis of W G 3 14 2 14 1 14 3 14 2...
- Q Let y and u B Write y as the sum of a vector in Span u and a vector orthogonal to u y tr Type an integer or simplified fraction...
- Q of the matrix Find the characteristic polynomial using either a cofactor expansion or the special formula for 3x3 determinants Note Finding the characteristic polynomial of a 3x3 matrix is not...
- Q 1 point Calculate the area of the parallelogram determined by the following vectors Area 5 2 0 4
- Q Let A be the following matrix A 0 1 1 0 a Let A R x3 What is the rank of A b Let F be the finite field of...
- Q ii Consider the equation T and hence 1 1 2 5 I 1 3 2 2 4 3 Using our results in 1 we see that the determinant in the...
- Q 12 If B B and B are bases for R and if PA and Pa 3 then Pa B 2
- Q Problem 7 8 points Consider the ordered bases B a Find the transition matrix from C to B 188 b Find the coordinates of u 4 7 and 1 6...
- Q Solve the equation for x 5x x 21 x 20 The solution set is
- Q Find the matrix P that orthogonally diagonalizes the matrix A A B D P P P P 3 3 2 6 3 2 3 3 3 3 3 2 3...
- Q 1 Let A a xn be symmetric and positive definite Show that a a 0 i 1 2 n b a a a i j 1 2 n
- Q Use technology to solve the system of equations if a solution exists If there are infinitely many solutions express your answers in terms of x4 as in Example 3 there...
- Q c Let B 3 3 41 04 i Use Givens rotations to reduce B to a row echelon form Your answer should include each Givens matrix you use ii Find...
- Q Use the following matrix to perform the indicated operation when possible If not possible enter IMPOSSIBLE into any cell of the matrix 0 1 3 532 023 A Find A
- Q Use the matrices below Perform the indicated operation 8 5 3 1 0 0 5 8 6 010 1 6 7 0 0 1 A Find AI
- Q 3 Are U and V orthogonal with respect to standard inner product on M22 If not find the cosine of the angle between them Find d u v v 23...
- Q 2 Using the inner product on R2 generated by matrix A 3 find u v for the vectors u 1 2 and v 2 4
- Q The three vectors 2 3 and n3 define the three planes 3 x R n x 6 x R n x 6 x R n3 x 10 What is the...
- Q 1 Choose three different non zero integer values for the empty boxes and find the determinant of the resulting matrix 4 marks A 2010 420 3 1 5 3 0...
- Q for the matrix A below find a value of k so that A has two basic eigenvectors associated with the eigenvalue A 3 k 0 0 0 4 14 1...
- Q 3 Use SOHCAHTOA to find the missing side a and angle b 5 marks 3 b Height of kite 10m Length of string 30m a Find b AC Anglex 4...
- Q and a bass p 2 g for the vector space f x P 1 f 1 where Paarl is the vector space of polynomials in a with degree less than
- Q For the matrix of transition probabilities 0 6 0 1 0 11 P 0 3 0 7 0 1 0 1 0 2 0 8 find p2x and p x...
- Q c Show that the basis of R is orthonormal 2 2 0 U W 2 2 2 6 6 3 V 2 21 3 3 Find the coordinates of 1...
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