Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

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 an LU factorization of the matrix A (with Lunit lower triangular). 4. A = -4 -3 L U

A: We have to find L and U matrix.

Q: Find the LU factorization of the matrix A, where 3 -5 2 3 2 -2 A = -1 -6 1 -1 -4 1 2 1 2.

A: We know that A = L U where L is the lower triangular matrix and U is the upper triangular matrix.

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

A:

Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

Q: 32. Construct a nondiagonal 2 x 2 matrix that is diagonalizable but not invertible.

A: .

Q: The 2 ´ 2 identity matrix is:

A: To find:

Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 A= 12 2 -0 12 8 4,

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Q: Find the inverse of the matrix using Gauss Jordan method?

A:

Q: Suppose AB = I, . Show that the equation Bx=0 has only trivial solution. Explain why the matrix not…

A: Suppose that AB=In (then x n  identity matrix). The objective is to show that, the equation Bx=0…

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

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

Q: 5 -1 5 1 6. -1 6 2

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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: 4. Determine ij, iz and iz by using the Inverse Matrix Method.

A:

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: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (а) (3, —4), (b) (1,2).

A: Find a 2x2 orthogonal matrix P whose first row is a multiple of(a) (3,-4) (b) (1,2)

Q: Find a 2 x 2 matrix such that -3 1

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Q: If A is any 5 by 5 invertible matrix, then its column space is __ . Why?

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Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

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

A: Given matrix combination is B = A + I

Q: What does it mean to say that A is a matrix with dimensionm  n?

A: A matrix is a rectangular array of elements arranged in rows and columns. The size of the matrix is…

Q: Use the Gauss-Jordan method to find the inverse of the given matrix (if it exists).

A: Given: 1514

Q: 2. Determine the matrix X, such that:

A: Solution:-

Q: Let A be 5x1 matrix. Knowing that Rank (A) = 2. Then Nullity(A) is equal to: O 2 ONone of these

A: The solution is given below in the next step:

Q: Define what it means for a function Q : R" R to be a quadratic form. Furthermore, explain how we…

A: The quadratic form is one of the most important parts of linear algebra. Quadratic means degree two.…

Q: Find the inverse of the matrix by Gauss-Jordan Elimination (using an adjoined matrix). (If an answer…

A:

Q: Let r1, .. r,be vectors in R", and let Q be an m xn matrix. Write the matrix Qr, Qr, as a product of…

A: Given:Let r1.......rp be vectors in ℝnLet Q be an m×n matrix Qr1.......QrpR=r1.......rpQ=Q…

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

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Q: To divide the LHS by a matrix on the RHS, what steps do you follow?

A: To find: To divide the LHS by a matrix on the RHS, what steps do you follow?

Q: ers such that p2 e matrix

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Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 6 -2 -4…

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Q: 3 (i);- 2

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

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Q: Let A be an m xn matrix. Explain why the matrix ATA is symmetric.

A: A square matrix is symmetric if  A^T = A

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: Find an LU factorization for the matrix: 1 2 1 2 1 2 -2 0 1

A:

Q: Find 2x2 invertible matrices A and B such that A + B not equal to 0 and A + B is not invertible.

A: Wee need to find matrix A and B and do their addition and find invertible

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 the LU factorization of the matrix A, where 3 -5 2 -2 A = -1 -6 1 -4 1 2 1 2. 2.

A: Given matrix is A=−23−5232−22−1−61−1−4121. We have to find the LU-factorization of the matrix A. By…

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

A:

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

A: Solve by matrices

Q: Reduce the quadratic form 3x2+5y2+3z2-2yz+2zx-2xy into a canonical form of the matrix.

A: Given quadratic form 3x2+5y2+3z2-2yz+2zx-2xy.

Q: Find the inverse of the elementary matrix.

A: Given matrix, A=0110

Q: Compute the matrix exponential e At for the following system x' = Ax. x'1 = 6x1 - 2x2, x'2 = 2x, +X2…

A: Step:-1 Note:- If A is diagonalizable matrix that is,  there exist an invertible matrix P and a…

Q: Since it is, find the matrix P ^ -1 by using the adjoint matrix of the P matrix.

A: We are given that  We need to find the inverse of p-matrix

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…