find a 3 x 1 matrix x with entries no all zero such that Mx = 1x and            [ 1 2 -1 M =      1 0 1             4 -4 5 ]

Q: Give the matrix X such that -1 -1 3. -2 X = 0. -5 Type DNE 4. -5 1 0. 0. if such a matrix does not…

A: Given: 02-135-2-3-51X=-1000-50004 If AX=B, then X= A-1B. We know that A-1=adjAA and adjA= cofaijT

Q: Find a 3 x 3 matrix A such that Ax = 9x for all x in R3. A II

A:

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

A: Singular matrix mean its Determinant is equal to 'zero' .

Q: Express the invertible matrix (1 2 1 10 1 1 2) 1 as a product of elementary matrices.

A:

Q: Find a matrix A such that e [-] -2 is a solution for Ax= x'.

A:

Q: At Compute the matrix exponential e for the system x' = Ax given below. x₁ = 37x₁ - 36x₂, x 2 = 34x₁…

A:

Q: For which value of x is the following matrix not invertible: 1 1 3x A = 3x 3x 3x 3x 3x O 2 4 O1/3 1

A:

Q: (4) For the zero-one matrices A = and B = calculate %3D 0 0 1 1 (а) АЛВ (Ъ) АоВ (с) ВОВ

A: 4) Note:  AΛB = [aijΛbij] =[aijbij] , known as meet of A and B, only possible if matrix have same…

Q: Suppose that A is a singular matrix and A is A = [ k 2 0 0 (k+1) 2 0 1 k ] Find…

A: Singular Matrix

Q: . Let A be an invertible matrix such that A = NOT 2 0 1-1 201 1 01 2134 Solve the system (2A2)x= b,…

A:

Q: a) Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

A:

Q: Find 2 X 2 matrices A 0 and B # 0 such that AB = 0. Can you find a matrix A + 0 such that A2 = 0?

A:

Q: -2 1 2 1

A:

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: Suppose A is a 2 x 2 matrix such that A and 1 A What is A-1?

A:

Q: Let A be an Xn matrix satisfying A-34 +I= 0 where 0 is the nXn zero matrix. Then A = A² - 31, A= =…

A: The objective is to choose the correct option for inverse.

Q: (4) Given a matrix X of independent variables, psudo-inverse X† is defined as (X"X)-'x" (a) If X is…

A: If a matrix is of order (mXn) then transpose of A is of order (nXm).

Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

A:

Q: For which value of x is the following matrix not invertible: 1 1 2x A = 1 2x 2x 2x 2x 2x 4 1 -1 1 2

A: For a matrix A to not be invertible: dat(A) = 0.

Q: FInd the Solution by Considering Attachment.

A: The method of mathematical induction can be followed to prove above result. Now, The given matrix is…

Q: Find the singular value decompostion of the matrix. 1 1 -1 -1 1

A:

Q: If A is 3 x 3 matrix such that 1 -3 1 1 A 1 -3 Al 1 A 1 1 -3 -2 -4 then A is diagonalizable. Select…

A:

Q: Find the singular values of the given matrix.

A: Given matrix

Q: If A is 3 x 3 matrix such that (A + I3)² = 0 %3D Show that: A is invertible.

A:

Q: Suppose A is a matrix that is 0 0 0 0 0 0 0 0 0 What is I-A

A:

Q: Find x such that the matrix is singular. A = -3 -4 X =

A: Matrix is said to be singular , if and only if the matrix has determinant is zero Det(A) = 0

Q: Let Q be an m xn matrix with n >n and orthonormal columns, then we have both QTQ = I, and QQT = Im…

A:

Q: Construct the matrix with rank one that has Av = 12u for v = ½(1, 1, 1, 1) and u= ½(2, 2, 1). Its…

A: Given: Let A be a given matrix. rank (A) = 1 To find: The only one singular value for  Av = 12 u .

Q: Find a 3 x 3 matrix A such that A A A A = 0 0 = 2 5 0 3 and

A: Given A100=-1-41,  A010=251  and A001=003

Q: Construct a 3 × 2 nonzero matrix A such that: Ax = 0 has only the trivial solution.

A:

Q: Find a 2 x 1 matrix x with entries not all zero such that 4 1 Ax = 4x, where A = 0 2 [Hint: Rewrite…

A: Find a 2×1 matrix x with entries not all zero such that Ax=4x where A=4102.

Q: Reduce the quadratic form x2+y²-9xy into a canonical form of the matrix.

A: The given equation is x2+y2-9xy. The standard equation is ax2+by2+cz2+2fyz+2gzx+2hxy. The…

Q: Suppose that A is 2x2 matrix with eigenvectors V, which correspond to A, = 3, A2 = 2 respectively.…

A: Given information of 2×2 matrix A:eigenvectors: V1=2-3  correspond to λ1=3  ,…

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

A:

Q: Find the augmented matrices of th e linear systems x +5y = -1 , -x + y = -5 ,2x + 4y = 4

A:

Q: Find x such that the matrix is singular.

A:

Q: Find the singular values of the given matrix.

A:

Q: Find the value of k such that matrix A is singular: (1 2 A = | 5 -1 2 6. k.

A: Singular Matrix: A square matrix that is not invertible is called singular or degenerate i.e., it is…

Q: 2. Write the quadratic function f(x,,y;)=-3x; +2x,x, – 3x; – 4x, – 4x, +6 in matrix form as f(x) =…

A:

Q: Find the dimension of the null space of the given matrix A. 1. -1 4 A = 2 3 -2 1 2 -2

A:

Q: Find a 3 x 3 matrix A such that Aa = 9x for all a in R³

A: We have to find matrix A such that Ax = 9x

Q: Find the singular values of the given matrix.

A:

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

A: Given: A2=1001

Q: Find a 3x1 matrix X with entries not all zero such that AX = X , where [1 0 -1] A =1 0 1 4 -4

A:

Q: Find the singular values of the given matrix.

A: Consider the given matrix, A=2102

Q: Find x such that the matrix is singular. x 5 A = -3 2

A:

Q: Suppose that A is a 4 x 4 matrix such that det A = 10. Enter the value of det(A³).

A:

Q: 1. Use matrix inversion to solve for x, y, and z if: x + 2y + 2z = −1 y − x − z = 0 2z + 3y + 3x = 1

A: see below the answer

Q: Find a 3×3 matrix A such that  Ax=4x for all x in R3.

A: To find a 3×3 matrix A such that Ax=4x for all x in R³