Find all 2 x 2 matrices with real entries of the form a b A = such that A? = I2.

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

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Q: Let A be an nxn matrix and B= A+ I, where / is the identity matrix, then it is possible for A and B…

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Q: A? 0 0 A =

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

A: Given matrix is A=2   11   2 and condition is Ax=3x

Q: Determine which matrices are in reduced echelon form and which others are only in echelon form. 0 0…

A: A matrix is said to be in row echelon form if All rows consisting of only zeroes are at the bottom.…

Q: Let A and B be nxn inversible matrix. Prove that AB is invertible and (AB)-1=  B-1A-1.

A: Let A and B be n x n invertible matrices, with inverses A-1 and B-1, respectively.

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

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Q: Let A and B be invertible 5-square matrices such that A| = 4 and B = 2. Then |2A. B 2 %3D

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Q: Find x and y such that the rank of matrix A is 2. 1 0 a – 1 0 у- 2 г+1 -5 A = 4 x = Ex: 5 Ex: 5 С y…

A: We are using rank nullity theoram  Rank(A) + nulity(A) = number of coloumn in A.

Q: ) Find a matrix A such that 3 A -3 1 1 EEE A =

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Q: Show AB + BA for the indicated matrices. A= 2 3] B = -1

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Q: Find two different 2 × 2 matrices A such that

A: Given:               A2=1001

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

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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?

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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: Find x such that the matrix is singular. [ х 7 A = -5 2 X =

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Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

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

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Q: Let A be the matrix a- [}] 3 1 A = Which answer is correct for the A ?

A: GivenA=3121

Q: Г1 3 2 5 1 [3 4 2

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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…

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Q: 2. Assuming that all matrices are nxn and invertible, solve for D. CTB-A'BACDA²²B™C-2 = CT

A: We use properties of invertible matrices.

Q: Find two 2 × 2 matrices A such that A2 = I.

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: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3 -2]…

A: A=13-223001-1

Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1 A =0…

A: Given,

Q: = (: ) such that A² = 13. Find all 2 x 2 matrices A

A: Given,

Q: Find 2 × 2 matrices A and B such that AB = O but BA ≠ O.

A: To Find: 2 x 2 matrices A and B such that AB = O but BA is not equal to O Here O is a zero matrix…

Q: Let p(x) = x³ – 2x + 4 and compute p(A). |2 A = |0 -3 4 NOTE: Write the elements of the matrix…

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Q: Find two different 2 × 2 matrices A such that A2 = O .

A: Let A=abcd be the 2×2 matrix.

Q: Prove that the matrices and a a a 0. a 3. a are Similar ( These 2 matrices are not deagonalısable)

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Q: Let A and B be n × n matrices and let C = A − B. Show that if Ax0 = Bx0 and x0 = 0, then C must be…

A: Consider the A and B are n×n matrices and C=A-B. If x0=0, Ax0 =0 and Bx0 =0 are nontrivial…

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

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Q: Determine the dimensions of Nul A and Col A for the matrices. A =

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Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 1 -1] A…

A: NOTE:We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: find a 3 x 1 matrix x with entries no all zero such that Mx = 1x and            [ 1 2 -1 M =…

A: Consider a system of homogeneous equations. A system of equations can be solved by eliminating some…

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 X1 -1 -5 X2 II

A: Let us consider the system of differential equation X'=AX then the solution of system of equation is…

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: Let A be an nxn matrix and B= A+I, where / is the identity matrix, then it is possible for A and B…

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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

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

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Q: Find two unequal 2 × 2 matrices A and B such that

A: The objective is to find two different 2 × 2 matrices A and B such that AB=1001 Let A=pqrs, B=tuvw…

Q: Find two 2 × 2 matrices A such that A2 = O.

A: to find a matrix A

Q: Let A and B be similar invertible matrices. Show that the matrices A-1 and B-1 are similar.

A: If A and B be similar invertible matrices then to show that the matrices A-1 and B-1 are similar.