Algebra question and answers for August 12, 2023
- Q 2 Let A 1 2 2 1 23 11 2 2 3 H LAW 1 1 1 2 3 2 0 2 a Applying the QR factorization to solving the...
- Q 2 4 MARKS Find the standard matrix for the operator on R which contracts with factor 1 4 then reflects about the line y x 01 1 4 1 1...
- Q 1 point Let W be the set 1 3 Let W be the set 2 3 2 9 0 Determine if W is a basis for R and check the...
- Q Given a b 40 A 0 3 0 10 2 Find the eigenvalues and bases for the eigenspaces of A Is A diagonalizable Justify your answer
- Q 1 Compute the determinant of the following 5 x 5 matrix 1 1 1 1 1 2 A 1 1 1 3 3 4 2 23 24 3 3 33...
- Q 1 point The matrix 4 8 4 4 0 2 2 has two real eigenvalues one of multiplicity 1 and one of multiplicity 2 Find the eigenvalues and a basis...
- Q 1 6 points Find the inverse matrix of each of the following matrices if it exis A 002 010 1 0 0 B 3500 1200 0001 0010 C 35 00...
- Q Define the linear transformation T R T u T v R by T x 6 6 A 249 12 1 8 Ax Find the images of u 2 4 5...
- Q 7 LU V Ive 1 L 30 17 02 27 08 4 O 4100 3216 1 1 1 1 Azz for the system with out multibying Lti
- Q 1 point Consider the linear system a Find the eigenvalues and eigenvectors for the coefficient matrix A 1 y 3 i 04 H 4 G and 1 5 5 b...
- Q Esercizio 2 Let s consider the following matrix A 2 a Find a basis of the kernel of A b Find the characteristic polynomial and eigenvalues of A e Find...
- Q 24 5 pts Show that the equation Ax b does not have a solution for all possible b where 1901031 202112190103A 00 0 A 2 2 and b b 3...
- Q The vectors B 2 B 1 18 5 3 form a basis Find a vector x given the B coordinates of x are
- Q Solve 18 II 2 1 2 608 3 17 12 X 13 30 51
- Q 1 2 A 2 1 L2 2 27 2 FIND A 4A 11
- Q Let A QR be the QR decomposition of A where A QR 1 2 0 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1...
- Q Which of the following is the trace below 00 01 10 trace AB7 where A CA 0 0 and 8 2 1 2 B 0 10
- Q tx 5 H 2 3 and y yll yll yll 3 3 Compute
- Q Let C 1 a b b Compute QQ and so find Q if Q 0 Q a b c ba d C d d C c d a
- Q Let A 123 1 28 and v G Also let H be the two column vectors of A Compute A and A a Av b 44 5A What do you...
- Q Consider the linear system 22 12 10 2 a 142 a For which value of a will the system have no solutions b For which value of a will the...
- Q 1 point Let T R R be a linear transformation such that 2 0 9 0 4 0 0 T Find the following 7 0 8 3 7 Hint First...
- Q For k 0 use the row reduction method to find A 1 A if given 12 0 13 1 13 k 1
- Q 1 For k 0 use the row reduction method to find A if given 1 2 0 3 1 3 k 1 A 1 1
- Q Let 1 3 0 1 k k 0 31 Find the values of k for which A is not invertible NOTE Enter all values exactly Number of answers 0 A
- Q Consider B ir Ma 3 what is Me B 1 and 1 A ve vc B M 2 ve 11 22 0 v c 3 C are bases for R2
- Q Find a basis for the nullspace of the matrix If there is no basis enter NONE in any single cell 13 6 4 8 6 3 2 4 2 1...
- Q Let 4 1 2 B 2 C 113 1 D 3 Evaluate each of the following if possible If it is not possible justify your answer Show all your work...
- Q Let u 3 2 3 and v 2 4 2 Find ux v
- Q Consider A What is the maximal order of a minor A 1 B 3 C 4 5 0 1 5 2 3 4 1 2 1 3 3 1 D...
- Q Let A 272 1456 Decide whether the matrix A is invertibile and if so use the adjoint method to find its inverse Enter as a matrix exactly in fractional from...
- Q These points are linear Find the slope x 3 2 1 012 y 3 2 10 12 slope Enter
- Q Let A A 11 If the matrix is invertible use the adjoint method to find its inverse If the matrix is not invertible indicate that using the checkbox NOTE Write...
- Q 5 In the diagram the inscribed angle LABC has a measure of 50 AB BC and the radius of the circle shown is 10 units What is the length of...
- Q 1 point Let Define the linear transformation T R R by T A Find the images of u H 4 T T u 0 7 0 BH A 0 02...
- Q If V V2 V3 is a basis of R3 show that U 42 433 is also a basis of R3 U V U V V U3 V V3 2 The...
- Q Use Cramer s rule to solve the system y z 4 X y 2z 14 x 4y 2z 17 X Find the determinants D x 0 0 0 0 Select...
- Q Problem 13 7 points Find the eigenvectors for the matrix A B 1 1 9 6 D C C E 4 0 1 03 0 102
- Q c Find a basis for the solution space for AX 0 where A What is the dimension for this solution space 1 2 2 2 1 1 1 1 2...
- Q Let A PDP 1 and P and D as shown below Compute A4 P A4 13 25 D 1 0 03
- Q A p 2 B F 3 Given A use the Frobenius inner product and the corresponding induced norm to determine the value of each of the following A B and...
- Q 1 point For which value of k does the matrix A 58 5 6 have one real eigenvalue of multiplicity 2 k
- Q 2 Solve the system of algebraic equations x 2x 0 X 2x x 1 3x x x 6 by Cramer s method Check the answer
- Q below Thanks 1 Confirm by multiplication that is an eigenvector of A and find the corresponding eigenvalue 1 2 1 X 32 a A 4 0 1 b A 2...
- Q a Solve the following equation for matrix X 0 0 0 P 000 1 1 0 23 RX B 3 x 2 12 0 1 1 23 12 1 1...
- Q 3 Construct an orthonormal basis for the subspace of R4 W span x1 x2 x3 15 x 0 3 4 0 C x2 70 2 1 2 C X3 1...
- Q 1 point Which of the following sets of vectors are linearly independent Check the boxes for linearly independent sets 8 0 A B 0 7 5 1 2 4 2...
- Q Which of the following is NOT in the span of x and y 2 1 1 1 3 8 2 3 H 3 5 Y
- Q Find the rank and nullity of the matrix then verify that the values obtained satisfy Formula 4 in the Dimension Theorem 4 69 24 10 11 0 2 4 2...
- Q Question 2 4 points Find a QR factorization of A 1 1 1 2 2 2
- Q For the encoding matrix 13 2 5 3 10 A 29 54 6 19 decode the message GE 42 109 433 198 181 which gives a six character word 797
- Q 2 1 13 52 26 find an orthogonal basis under the Euclidean inner product Let 3 112 Orthogonal basis V x a Ex 1 23 113 3 V 3 b...
- Q Let W Span x1 x2 where 1 and 1 3 1 3 2 3 Compute the Orthonormal Basis Using Gram Schmidt Process
- Q Express each column vector of BB as a linear combination of the column vectors C C2 and c3 of B 3 4 2 B 0 1 6 5 Enter first...
- Q Use Gaussian Elimination to carry the following matrix to a REF 2 31 2 4 5 1 1 4 2 3 7 What are the positions of the pivots 1...
- Q 1 Let A a n be symmetric and positive definite Show that a a 0 i 1 2 n b a aa i j 1 2 1
- Q 1 A network of six one way streets A B C D E F is shown in the following diagram where 100 cars per hour enter at streets A and...
- Q What is the image of X 1 A 2 32 B 2 under the linear transformation T where I is the reflection across X2 X1
- Q The linear transformations T R R and T R R are defined by T1 X EDH X3 T X2 What is T T 2 W A 2 B 7 X1...
- Q 7 Solve the inequality set Graph the solution on a n 14 x 5 O x 9 or x 19 O x 9 or x 19 O x 9 or...
- Q 8 Find the points on the surface z xy 1 that are closest to the origin using LaGrange multipliers
- Q thy the ver ex or Remember y ax bx c O 9 48 O 4 31 O 7 84 O 3 4 by 10
- Q Using the discriminant state the number of soluti For the following equation 3y 18 one real root two real roots three real roots O no real roots Using the discriminant...
- Q Solve the system if possible by using Cramer s rule If Cramer s rule does not apply solve the system by using another method Write all numbers as integers or...
- Q Use the Gram Schmidt process to produce an orthogonal basis for the column space of matrix A An orthogonal basis for the column space of matrix A is Tyno a...
- Q 4 The following cyclic subgroups are all isomorphic the multiplicative group i in C the additive group Z and the subgroup 6 1 of S 23 2 3 4
- Q Part D Application 20 marks Full Solutions are required Consider the vectors u and w If 2 4 8 4 2 1 1 5 and W 1 1 1 find...
- Q 14 5pts Write the base four number shown below in base ten 10
- Q 5 2 1 and y 2 4 6 find the vector projection of y onto x 1 10000
- Q If possible find AB If not possible enter IMPOSSIBLE in any cell of the matrix 0 12 483 8 05 B 7 1 8 AB A 000 11 State the...
- Q 7 Suppose A is an n x n invertible matrix and A is an eigenvalue of A Suppose x is an eigenvector of corresponding to A a Show that A0...
- Q Let A be a diagonalizable n x n matrix and let P be an invertible n x n matrix such that B P AP is the diagonal form of A...
- Q Write the system of linear equations as a matrix equation AX B and use Gauss Jordan elimination on the augmented matrix 4 B to solve for the matrix X X1...
- Q Let the linear transformation T R R3 and S R3 R4 be defined by T x y x 2x y 3x 4y S x y z 2x z 3x z...
- Q 3 1 A 2 10 compute inverse matrix A 3 0 2 1 5
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