Algebra question and answers for August 16, 2023
- Q x 10 y 2 Hayja dre ot x yja dy c y
- Q Total number of possible passwords 26P X 10P3
- Q Given 9 x b y4 cG To find Maximum value of ny
- Q Let A 1 1 0 0 1 o and B 0 1 0 0 0 ol Are A and B similar matrices f they are similar find matrices C and...
- Q 3 A 2 J 1 31 5 2 2 7 3 2 Find the QR de composition of the H
- Q Lethod Solve the following system of equations using the Gauss Jordan elimination 3x 4y z 4w 1 5x 2y 2z w 6 x y 5z 3w 2 2xy 3z2w 0
- Q c It is given that a 3 3 matrix B has the following eigenvalues with corresponding eigenvectors w A1 95 w W1 19 2 14 12 95 W2 20 Explain...
- Q In Problems 21 24 the given vector functions are solutions to a system x t Ax t Determine whether they form a fundamental solution set If they do find a...
- Q a Timex c G h T kc G h Putting the dimensions in the above relation M L T LT 1 M E T PM T M L T MY...
- Q If cos 50 cos 0 sin 30 and 0 0 then 2x x 7 3 11x 3 12 12 Give your exact answers as a list separated by commas Question...
- Q ssuming A is a square matrix that satisfies the condition A2 3A 21 0 find all such A and their inverses
- Q Exercise 4 25 marks A company produces heaters of two types called S and L The wholesale price is 40 per heater S and 88 per heater L Two time...
- Q Prove the following identity without evaluating the determinants e s a b d C f e b a b c d
- Q 4 Solve the system of linear equations x y z w 5 2x 5y z 5w 6 3x 2 5w 1 x 3y 3z 5w 25 a b C d...
- Q 4 Start with Po 0 0 0 and use Gauss Seidel iteration to find Plc for k 1 2 3 Change the order of equations if necessory to make coefficient...
- Q Explaining Why a Set Is Not a Basis In Exe 15 22 explain why S is not a basis for R 15 S 1 3 0 4 1 2 2...
- Q 13 10pt Find a 3 x 3 matrix U so that the matrix is diagonal 100 120 13 3 1
- Q Perform the elementary row operation 14 2 35115 53 5 Resulting matrix R3 R3 R3 on the given matrix Write numbers as integers or simplified fractions 4
- Q Perform the elementary row operation 3R R on the given matrix 1 4 9 4 3 0 6 i Resulting matrix 0 X S
- Q y n 1 to Tn 1 0 satisfying the Given any initial values y to ro there always exists a unique solution to y n t a y n 1...
- Q nd the matrix A for T relative to the basis B T R 1 11 3 1 2 2 R T x y z x y 4z 4x y z...
- Q 3 If T R R is a linear transformation the vectors e e2 and e3 span determine a unit cube of volume 1 cubic unit and the vectors T e...
- Q Verify that X t is a fundamental matrix for the given system and compute X t Then use the result that if X t is a fundamental matrix for the...
- Q 1 For the following linear programming problem Minimize z 4x 6y subject to x 3y 25 2x y 24 20 y20 i Solve it using any method not forgetting to...
- Q 1 2 FHI Let u 1 2 4 1 2 2 U u u W be the column space 0 of U and w be the orthogonal projection of y...
- Q Solve the system of linear equations and check any solution algebraically If there is no solution enter NO SOLUTION If the system is dependent set a and solve for x...
- Q s a b of GL 2 R such that ab bc 1 Show that H is a Let H be the set of elements subgroup of GL 2 IR b...
- Q Find the eigenvalues and eigenvectors of the linear transformation T P P given by T ax b 6a 10b x 2a 3b Eigenvalue 2 Eigenvalue A Ex 59 Eigenvector 5x...
- Q Find the plane of reflection of the following pure reflection map Q 3 ON ON AIN 7 7 6 6 2 2 191201 7 21 37 67 7
- Q Use the Gram Schmidt orthonormalization process to transform the given basis for R4 into an orthonormal basis Use the Euclidean inner product for R4 and use the vectors in the...
- Q e graph shows the number of words in millions in a particular government document for selected years from 1950 through 2000 The data can be modeled by f x 0...
- Q et A 8 0 6 24 12 4 0 12 10 4 points Find the eigenvalues of A 6 points For each eigenvalue A of A find a basis for...
- Q Let A A a Determine the eigenvalues A and X2 of A where X d X 5 0 4 6 3 12 201 m x b Determine the algebraic multiplicity...
- Q 60 DE NA 60 2 80 407 80 B 2 5 C Q i ii B L 2 7 M2 PE iii 2 5 80P 4 B D M 99...
- Q tan f x 1 x 2 Answer tan x lx x 2 4 then find the value of x
- Q 3 Consider the matrix 2 a Find elementary matrices E and E such that E E A I b Use part a to write A as a product of elementary...
- Q f x x 4x x x 4 shown below D The graph as to the land ses to the hymn OC The graph rises to the left and falls to...
- Q Find the QR decomposition of the matrix M 1 25 7 2 3 21 1 3 1 4 1 2 3 25
- Q By using properties of determinants show that 10 a a 0 c 0
- Q 4 A survey of the ages of 90 retirees are organized in the table below V Veteran Veteran Non veteran TOTAL N Non veteran p E70 70 79 25 23...
- Q Given matrices A and B shown below find 8 A 4 B Give your answer as a matrix using the matrix tool Provide your answer below A B 3 0...
- Q 2 Consider the following model a identify matrices c A and b Max 2500x 1600x s t X 210 X 2 15 5x 9x 320 1x 2x 2 300 12x...
- Q 3 Find the standard matrix of the transformation T defined by 2x 3y z W 5x 2y z W2 3y 5z W3
- Q Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients i x 2x 8 ii 4s 4s 1 iii 6x 3 7x...
- Q Ex 5 R 5x1 x2 X3 x 2x3 2 ED T 3 1 Ex 5 R T X1 x2 Ex 5 Ex 5
- Q Solve the system in terms of the arbitrary variable x 3x 6y z 7 x y 3z 5 The solution set is 00 Simplify your answer Type an expression using...
- Q Subtract the following matrices 4 0 2 3 Give your answer as a matrix using the matrix tool 31 11 3 4 3
- Q Let A 3 1 0 2 0 2 4 a 4 points Find the eigenvalues of A b 8 points Find the basis eigenvector s for the smallest eigenvalue
- Q Solve the system State whether the system is inconsistent or has infinitely many solutions If the system has infinitely many solutions write the solution set with y arbitrary 5x 6y...
- Q Define T R R by T x A where matrix A Row1 4 3 Row2 4 3 Row3 4 3 What is the image of u 4 1 under this...
- Q 1 5 pts Let L R R2 be the linear transformation defined by L x a Find a basis for L S where S Span 2 0 1 0 1...
- Q Let A 1 3 1 Find an orthonormal basis of the column space of A 1 3 3 6 1 3 27 3 4 6
- Q 8 3 9 8 1 9 A B 6 9 7 8 2 AB AC A Ex 42 C
- Q 1 Two line segments AB and AC include an angle of 60 where AB 5 cm and AC 7 cm 3 1 Locate points P and Q on AB and...
- Q 4 Construct a pair of tangents to a circle of radius 4 cm from a point which is at a distance of 6 cm from the centre of circle Sol...
- Q 14 From the top of a tower n m high the angles of depression of two objects which are in line with the foot of the tower are a and...
- Q How Do You See It 38 The graph shows the total revenue and expenses of a company x years after it opens for business a Estimate the point of intersection...
- Q Uni tanily diagonalize the quadratic Form Q 21 2 2 23 4x 4x 4x 2x x2 221x3 2222 You have to show work clearly
- Q Let A D PT AP 23 8 8 8 11 16 Find an orthogonal matrix P with rational entries and a diagonal matrix D such that 8 16 11 P...
- Q Calculate by finding Jordan canonical form A 2
- Q 4 Show that if A is symmetric then so is PT AP for any compatible choice of F 5 Generalize Exercise 2 to the case of complex matrices
- Q find the singular value decomposition of each of the following matrices a b 1 Hi 1 12 2 1
- Q a b 3 a b 8 c d a be a basis for R x2 and 1 2 be a basis for P Let T R2x2 P be a linear...
- Q If A and B are similar matrices then both of them are diagonalizable True or False explain
- Q Find the characteristic equation and the eigenvalues and a basis for each of the corresponding eigenspaces c a the characteristic equation b the eigenvalues Enter your answers from smallest to...
- Q Solve the following system 2y z 7 x 4y 14 3x 2z 8 x 8
- Q T onsider the quadratic form q4 x y A where A I r the transformation T R R with standard matrix 10 04 x y ere 5 4 4 6...
- Q Question 3 12 points Solve each system State whether it is an inconsistent system or has infinitely many solutions If the system has infinitely many solutions write the solution set...
- Q 4 2 points Let V R and let W W is a subspace of V or not answers 21 1 1 1 13 9 Decide whether the without a proper...
- Q The matrix A 3 14 21 46 21 42 14 42 38 is diagonalisable with eigenvalues 3 4 and 4 An eigenvector corresponding to the eigenvalue 3 is Find an...
- Q 3 3 3 2 Write as a product of an orthogonal matrix and an upper triangular matrix Clearly show each step used in the process 4
- Q Consider the following system of linear equations 2y 2z2w 2 7y 3z 4w q 3x x 4y p z pw 8 where p and q are real numbers Using Gaussian...
- Q Find the B matrix for the transformation xAx where B b b A 6 2 1 b 1 2 The B matrix of the given transformation is b
- Q Define T P2 P by T p p 0 p 10 t p 11 t a Show that T is a linear transformation b Find T p when p t...
- Q cos x 0 2n x Select 2 correct answer s 00 11x 6 5333 No solution 7 02 12 2 55
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