1 -4 -9 1 3 -8 x = X3+x4 (Type an integer or fraction for each matrix element.)

Q: Show that the matrix A= -1 0 0 20 is diagonalizable over the set of real numbers and compute the…

A: Given

Q: Transform the equation u" + 4u' + 7u = 9 sin 8t into a system of first-order equations by making the…

A:

Q: Show that no 2 x 2 matrices A and B exist that satisfy the matrix equation [1 0 0 1 АВ - ВА. %3D

A: In this question we have to prove that no 2×2 no matrices the given matrix equation.

Q: Find an SVD of the matrix. -7 3 A = - 3 - 1 O (Type an exact answer, using radicals as needed.) A =

A:

Q: Describe and compare the solution sets of x, +2x2 - 6x3 = 0 and x, + 2x2 - 6x3 = - 5. X1 Describe…

A: Consider the solution

Q: Write out the system of equations that corresponds to each of the following augmented matrices. a) 2…

A: By bartleby rule first part has been answered Given augmented matrix is 2144-23526-11-1…

Q: Find x such that the matrix is singular. 4 A = -2 -6

A:

Q: Suppose 71 and 72 are solutions of the system A = b, where b + 0. Let aj and a2 be scalars such that…

A: Proceed as shown

Q: 星 Find a singular value decomposition of the matrix A. 港 -1 要 A = - %3D -1 星 里

A:

Q: Show that matrix A 5 1 0 5 cannot be diagonalized by using (λI-A)

A:

Q: Find an SVD of the matrix. - 2 A = - 2 - 1 A = (Type an exact answer, using radicals as needed.)

A:

Q: [A] Find all the minors and cofactors of the matrix 0. 2 1 A =| 3 -1 2 0 1] 4

A:

Q: . Show detailed solutions. Use Gauss-Jordan to solve the resulting system and indicate elementary…

A: The given functions are, p1=3+2x-x2p2=x+5x2p3=2-4x+x2 Let, c1,c2,c3 be the three scalars such that,…

Q: 2(b) Use matrix multiplication to find the reflection of (2, -6, 3) about (i) the xy -plane and (ii)…

A: We have been given the coordinates (2, -6, 3) which we have to reflect about xy and yz plane using…

Q: Find x such that the matrix is singular. 4-[94] A

A:

Q: Find the singular values the matrix:

A: Given:A=1201-21Singular values:detATA-λI=0

Q: b) Consider the matrix A = [a b] with a, b, c and d real-valued numbers. Under which condition(s)…

A: Negative definite: A square matrix is said to be negative definite if all the eigenvalues of the…

Q: Let A = 3 ů 5. positive definite show that the matrix A is. پول و مع دول ۷۵

A: A matrix is said to be positive definite if the given matrix is symmetric and all its eigen values…

Q: [2ß ß Find all the values of the parameter ß for which the matrix is 3 5B] Consider invertible.

A: The matrix is given as , A=2ββ35β find all values of β for which the matrix is invertible.

Q: Find x such that the matrix is singular. 4 X A -2-6 X3D

A: Given Matrix is, A=4x-2-6 we know that, A matrix is said to be singular if it's determinant is zero.…

Q: Please find the question attached.

A:

Q: Find a 3 x 1 matrix x with entries not all zero such that 1 2 -1 Ax = 1x, where A 1 1 -4

A: A=1  2-11  0  14-4  5 Now let x=abc be the required matrix. Now consider, Ax=1x⇒1  2-11  0  14-4…

Q: Find all the minors and cofactors of the elements in the matrix.

A: The given matrix is  A = 24-1032-570   The elements of the minor of the matrix A will be given by…

Q: Find the singular values the matrix:

A: To find the singular values of the matrix A=101-101-11 we will first find the transpose of matrix A…

Q: Prove that the quadratic equation A^2 - 3A = 2I hold true for the matrix A =  5  -6  -6        -1…

A: The detailed solution is as follows below:

Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 - 2xy- 2xz -…

A: The objective is to find the symmetric matrix and diagonal form of the quadratic form…

Q: Determine the cofactor of 2 in the matrix A = 1 9. 7 4 O-4 3. O -3 2.

A: Cofactor of any element aij is the determinant of the matrix formed by deleting row i and column j…

Q: a) ir(A - 1)1- ( -2) %3D Find the matrix A

A:

Q: Show that the matrix A = singular. 1 -2 3 4 0 5 0 is 60

A:

Q: FIND THE FUNDAMENTAL MATRIX AS W ELL AS THE FUNDAMENTAL MATRIX SATISFYING )- I x'= -4 %3D

A: For the solution follow the next steps.

Q: Let A be a real matrix such that the linear system Ax = 0 has a nonzero complex solution. Show that…

A:

Q: Use the definition of Ax to write the vector equation as a matrix equation. 3 4 - 2 7 -3 + X2 - 9 5…

A: Given vector equation- x13-501+x24-3-99+x3-267-6=7198 To write the vector equation in matrix…

Q: (b) Unitarily diagonalize the following matrix 3 -6i 6i 6 -

A: We have to diagonalize the given matrix A=3-6i6i-6 unitarily

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: Find a 2 x 2 matrix such that 5 1 1 0 2 1

A:

Q: 1. Find the matrix P that projects points in the plane onto the line 5x - 2y = 0

A: As per honor code, we are entitled to solve only one question at a time so I am providing the same.…

Q: Find x such that the matrix is singular.

A:

Q: Associated with every square matrix A is a real number denoted by |A| called the __________ of A .

A: |A| denotes the determinant of a matrix A. Hence,

Q: Let A be the 3×3 matrix of zeros. Describe all solutions to Ax​=0.

A:

Q: Find a 2 × 1 matrix x with entries not all zero such that

A: Given: Ax=3x, where A=2112 let's assume matrix x is x=ab

Q: Show that a. A is diagonalizable if (a – d)² + 4bc > 0. b. A is not diagonalizable if (a – d)² + 4bc…

A:

Q: X1+ 3x2 0 X1+2x2 +X3 0 X1 + X2 + 2x3 = 0 Show the reduced row echelon form (RREF) of the resulting…

A: Given system of equation written as,…

Q: Show that if B is a scalar multiple of the 2 × 2 identity matrix, then AB=BA for all 2 × 2 matrices…

A: Prove the following

Q: State Cayley-Hamilton theorem. Verify Cayley-Hamilton theorem for the matrix [1 A -17 1 -1 %3D 13 -1…

A:

Q: Show that it is impossible to find two real 2 x 2 matrices A and B such that AB - BA = dI where d…

A: Take A and B are arbitrary matrices and find AB-BA and analyse the diagonal elements

Q: 2 -3 is a solution of Ax = 0. -4 Construct a 4×4 nonzero matrix A such that the vector 5

A: We know Ax = 0, x =    2-3-4   5 Let us take A = a1a2a3a4a1a2a3a4a1a2a3a4a1a2a3a4

Q: Consider the 3 x 3 matrix 1 2 3 A = b а -1 2 3 where a, b and c are some unknown scalars. If…

A: We are given a matrix: A=123abc-123 we need to find a, b and c such that A13 =24, A12 =-19 and A33…

Q: Find a non-zero 2 × 2 matrix such that -5 -1 0 0 25 ||

A:

Q: (b) Show that an n x n complex matrix is unitarily diagonalizable if and only if it is normal.

A: By using Schurs theorem the answer is given as follows :

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.