Let A and B be two matrices of size 3 x3 such that det(A) = -2 and det(B) = 2. Then det(2A 2B") =

Q: Find two 3x3 invertible matrices A and B, such that A+B is not invertible.

A:

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: Let A, B be 2 x 2 matrices, C a 3 x 3 matrix and D a 1 × 1 matrix. Find the condition on these…

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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: Show that there are no 2 x 2 matrices A and B such that АВ — ВА —

A: Given- AB-BA=1001 To prove- That there are no 2×2 matrices A and B so that it can satisfy the above…

Q: 2x1- 3x2+ 2x3= 9 3x1- 2x2+ X3 = 4 X1 - 4x2+ 2x3 = 6

A: Given system of linear equations is ,                        2x1-3x2+2x3= 9…

Q: 4. Find the standard matrix for T where Ta2) =(2x,+x -2,).

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

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

Q: .

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Q: Find three non-trivial 2 x 2 matrices such that the square of the matrix is the zero matrix, i.e: A?

A: We want to find matrix A such that A2 = 0000

Q: Find two 3 x 3 matrices A and B such that det(A + B) + det(A) + det(B) Upload an image or PDF of…

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Q: What does it mean to say that A is a matrix with dimension m x n?

A: Our Aim is to tell that what is meant by a matrix A which is havingdimension m×n.

Q: Find an SVD of the indicated matrix.

A: The matrix is given of which SVD is to be calculated so,

Q: Let A be an n × n matrix in which the entries of each row sum to zero. Find ∣A∣.

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Q: What is 'a', if B as shown below is a singular matrix?

A: A singular matrix is a matrix whose determinant is zero.

Q: Let A be a 3x6 matrix of rank 3 then nullity of A equal 0 Select one: O True O False

A: From rank plus nulity theorem we know that : rank A + nullity A = the number of columns of A  From…

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: Suppose A and B are orthogonal matrices. Show that A", A-1, AB are also orthogonal.

A: we have given A and B are orthogonal matrices.  We have to show that the following

Q: If Aand B are invertible matrices of the same order, Then show that AB is invertible matrices.…

A: LHS   =  (AB)-1  RHS  =  B-1A-1 For    (AB)-1  =  B-1A-1 ,   RHS * inverse of LHS = i…

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

A:

Q: If A is a nonsingular matrix whose inverse is 4 find A.

A: Given  The  A  is a nonsingular matrix  whose inverse is 2141.

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

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Q: Let A and B be two matrices of size 3 x 3 such that det(A) = -2 and det(B) = 3. Then det(2A-'B") =…

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Q: Find a (2x2) singular matrix A that maps (s1, ss) into (s2, s6).

A:

Q: Let A = [0 1 0 0 ], A^(-1) is equal to: * Does not exist Identity matrix Null matrix

A:

Q: Let A, B, C be invertible matrices of order 3x3. Show that if AB = AC , then B =C. %3D

A: Let A, B, C be invertible matrices of order 3×3. To show that if AB=AC, then B=C.

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

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Q: Suppose A +A+I-0 where A is a square matrix then A= A -A-I -2A A-I CS Scanned with CamScanner

A: Now we will find A-1 . Where I is identity matrix.

Q: -) Let A, B be nx n symmetric matrices such that XTAX = X™BX for all %3D column vectors X e R". Show…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Find the augmented matrices of th e linear systems x - y = 0 ,2x+y=3

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Q: Find x such that the matrix is singular.

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Q: hat is the matrix for

A: Given, consider the two-tank system shown below. Each of the two tanks contains 200 gallons of water…

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

A: Here in this question find a 2×2 matrix that maps (2,2)  into (1,2). Here i attached solution of…

Q: Using only 0's and l's, find the number n of possible 3 x 3 matrices in row canonical form.

A: We have to make all possible row echelon form ( row canonical matrices ) of 3×3 matrix with 0 and 1…

Q: 6. Give an example of two matrices, A and B, neither of which contains any zero entries whose…

A: Below mentioned a example related to this, you can construct many.

Q: Show that no 2 × 2 matrices A and B exist that satisfy the matrix equation

A:

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 3 -4 -3 L = U = A,

A: The solution is given below

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: Let A be annxn matrix and B= A+T, where I is the identity matrix, then it is possible for A and B to…

A: Let λ be the eigen value of A. As B=A+I So, eigen value of B will be λ+1 which is not same as λ

Q: Let A be a nilpotent matrix of order n then A*n = 0 ) nxA = 0 A =nx1, l is Identity matrix

A: A be a nilpotent matrix of order n

Q: Find two nonzero matrices A and B such that AB= 0

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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: Find two different 2 x 2 matrices A such that 1 0 A? =

A: Given: A2=1001

Q: Which of the following matrices is positive definite?

A:

Q: Is it true that the sum of invertible n x n matrices is invertible?

A: Given: The statement is : Is it true that the sum of invertible n x n matrices is invertible? It is…

Q: Find the nullspace of the matrix given as; A=[1 -2 1; 2 -3 5; 1 0 7]

A:

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…