If A is a 2 x2 matrix such that det(A) = -3 and tr(A) = 5 then the characterestic polynomial of A is p(^) =x2 -5A-3 Select one: O True O False

Q: State the quadratic form of a general multivariate function in two variables and give the matrix…

A: Given problem is :   State the quadratic form of a general multivariate function in two variables…

Q: Suppose A is the 3 x 3 zero matrix (with all zero entries). Describe the solution set of the…

A: To prove  Ax = 0

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: Suppose that matrix A has dimension 5•3 and that matrix B has dimension 3•5. Decide whether product…

A: Given: The matrix A has dimension 5×3 and that matrix B has dimension 3×5. To Find: To decide…

Q: lues of a 4 x 4 matrix A are given by 2, 1,5, 4, the

A: We have to choose the correct answer from the given option according to the given condition

Q: Using only 0's and l's, list all possible 2 × 2 matrices in row canonical fom.

A: Row canonical matrix All zero rows, if any, are at the bottom of the matrix. Each leading non zero…

Q: Find inverse of matrix 1  2  3 0  4  5 0  0  6 Using augmented matrix  Show work

A:

Q: Find two 2 × 2 singular matrices whose sum is nonsingular.

A:

Q: Find a singular value decomposition of the 2 by 3 matrix with entries: 3, 0, 0 0, -1, 0

A: The given matrix is A=3000-10 The matrix can be calculated as ATA=900010000  It has eigen values…

Q: Create a world transform matrix that translates by 3, 5, 7 and rotates 80° about the x-axis.

A: Detailed explanation mentioned below

Q: The maximum value of the determinant among all 2×2 real symmetric matrices with trace 16 is

A: But they cannot be both negative as a+d=16 And the value of ad is maximum  a=8, b=8 Therefore

Q: Under which conditions an inverse matrix be defined for a matrix?

A: There are two conditions for matrix to be invertible.

Q: Using only 1, 2, and, 3 as coefficients, create a matrix of size 5x5 (with all coefficients…

A:

Q: A and B are 3,3 matrices. Lo lAl =-3 and IBl =2. SO phat is l-2A02|?

A: Properties of determinant:kA=knAAB=ABA-1=1A

Q: Show that when performing LU decomposition of an nxn element matrix for a set of linear equations,…

A: L U decomposition of a matrix is the factorization of a given square matrix into two triangular…

Q: How matrix notation helps in simplification of computations with systems of differential equations?

A:

Q: Find 3 x 3 upper triangular matrix with determinant 1.

A: 3×3 upper triangular matrix

Q: Find a sequence of elementary matrices whose product is the given nonsingular matrix.

A:

Q: There are sixteen 2 by 2 matrices whose entries are 1s and -1s how many of them are invertible

A: A matrix will be invertible if the determinant is not equal to 0

Q: Find an orthogonal matrix whose first row is (1/3,2/3,2/3)

A: The rows of an orthogonal matrix forms an orthonormal basis. Therefore, consider the extended basis,

Q: a() – 4 (6) - (1) - (-) - Find a 2 x 2 matrix A such that A

A: We have to find a 2 × 2 matrix A such that A12=A23=41 Let the matrix A = abcd

Q: Is the product of two elementary matrices always elementary? Explain.

A: To check product of two elementary matrices will be elementary or not.

Q: Suppose A is a 4 × 4 coefficient matrix. If possible, find the entries of a matrix T that perform…

A:

Q: Could a rref matrix look like | 1 0 0 1 | | 0 1 0 1…

A:

Q: What do 2 × 2 matrices represent graphically?

A: 2 × 2 matrices represent:

Q: Find a (2x2) singular matrix A that maps (3, 1) into (2, 4).

A:

Q: Use (ii) of the rank of a matrix by row reduction theorem to find the rank of the given matrix. (?…

A: The given matrix is 7-113.

Q: Two 2 x 2 invertible matrices can have a matrix sum that is not invertible.Determine whether the…

A: ''Two 2 x 2 invertible matrices can have a matrix sum that is not invertible''. We have to determine…

Q: A characteristic polynomial of a 4x4 matrix can have 5 different roots. True False

A: let us consider a 4 x 4 matrix in reference for understanding this question well.

Q: What is the characteristic equation of the matrix (10 5) ² ? 3 (Give the characteristic equation in…

A: Characteristics equation of the matrix

Q: Find inverse matrix using Gauss - Jordan Method if available 1 -2 4 0 8 -3 -4] A = 2 -1 ||

A:

Q: find if the vector x is in the range for matrix A

A:

Q: How can we determine the cofactor for each element in a matrix?

A: Query- How can we determine the cofactor for each element in a matrix? Answer-  The first step…

Q: If a 6 x 6 matrix contains 19 zeros, show that there are 4 zeros which are all in distinct rows and…

A: A 6x6 matrix has 36 entries. Given if a 6x6 matrix contains 19 zeros, then to show that there are 4…

Q: Suppose an organism moves down a sloped surface along the steepest line of descent, i.e., the…

A:

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

A:

Q: Find the greatest value of A that make the matrix 2 – 9 – A - A singular. – 6 -2 – X.

A:

Q: 4 For A= calculate A by using Adjoint Matrix Method. (Do not use any other method) 3 5

A:

Q: Using only these numbers ( 2,1,9 ) as coefficients, create a matrix of size 5x5 (with all…

A:

Q: Find the number of 3x4 matrices in row echelon form, with entires from F = Z/2Z

A: To find the number of 3x4 matrices in row echelon form, with entries from F = Z/2Z.

Q: Suppose an organism moves down a sloped surface along the steepest line of descent, i.e., the…

A: Topic = Derivative

Q: singular values and SVD of a n × 1 matrix

A:

Q: The i-th column vector of an AB matrix product can be calculated by multiplying A by the i-th B…

A: True Because take A=a11a12a21a22 and B=b11b12b21b22 Then the product of AB is,…

Q: V3 Express 1 as a product of elementary matrices.

A: Solve by matrices

Q: Find two 2 × 2 nonsingular matrices whose sum is sin- gular.

A: From the given question,, To find the two 2 × 2 nonsingular matrices whose sum is singular.

Q: Find a sequence of elementary matrices whose product is the nonsingular matrix below.

A: Given non-singular matrix is :                                                          2-410   To…

Q: State the quadratic form of a general multivariate function in three variables and give the matrix…

A: A quadratic function f : R→R has the formf(x)=a.x2Generalization of this notion to three variablesis…

Q: Find out two examples for each types of matrices and write down it's order also

A: