Let 1 1 0 20 2 A 1 1 (a) (Ъ) you have used in (a); Compute A-1; Find the elementary matrix corresponding to the first row operation

Q: Find an LU factorization of the matrix A (with Lunit lower triangular). 4 -8 8 -4 A = 8 - 14 11 -5…

A:

Q: Find the characteristic equation of the matrix by inspection. 4 2] -6 0 0 6 0 0 5] 4 -9 LO

A:

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

A:

Q: Find an LU factorization of the matrix A (with L unit lower triangular). 2 -4 A = 4-4 3. - 1 18 -3

A: The LU factorization of a matrix A is writing A as the product of matrices L and U, where L is a…

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

A:

Q: Find the greatest value of A that make the matrix 2 – A 2 A singular. -6 5 – A

A: Eigenvalues and determinants

Q: The multiplicative identity matrix of order 3 is I3 =_______.

A: Let the Identity matrix be…

Q: Show that matrix A 5 1 0 5 cannot be diagonalized by using (λI-A)

A:

Q: If A is a rank one matrix, the second row of R is ___ . Do an example.

A:

Q: Determine the cofactor of a13 in the matrix. 2 -4 A =5 4 4 -4

A:

Q: .

A:

Q: Disprove that the rank of a matrix is equal to the number of nonzero rows.

A:

Q: 3. Determine whether the matrix is elementary. If it is an elementary matrix, state the elementary…

A:

Q: -2 1 2 1

A:

Q: 2. Consider the 6 x 8 matrix [1 3 0 0 0 0 1 0 2 0 5 -3 0 0 0 A 0 0 1 4 -7 -9 00 0 0 0 0 0 0 0 0 0 0…

A:

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

A:

Q: 8. Let A be a matrix 4 0 0 0 0 4 0 0 0 0 2 0 1 0 0 2 Determine if A is diagonalizable, and if…

A: Matrix A is diagonalizable if there exists an invertible matrix P and a diagonal matrix D, such that…

Q: When the inverse of a matrix is multiplied by the original matrix, it produces the: A. matrix of…

A:

Q: 2 Discuss whether the matrix A 1 2 0 is diagonalizable or not. -3 5 2 ||

A: A matrix is said to diagonalizable if for every eigen value's algebraic multiplicity is equal to its…

Q: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

A:

Q: Find a 3 × 1 matrix x with entries not all zero such that

A:

Q: Find the characteristic equation of the matrix by inspection. 2 -5 9 6 -3 0 0 4 0 0 8

A: Given that: 2-5960-30000400008 The characteristics equation is given by the formulas, detA-λI=0

Q: Show that any nX n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

A: To show that any n x n matrix can be written as the sum of a symmetric matrix and a skew-symmetric…

Q: Find a matrix B in reduced row echelon form that is rowequivalent to A, using elementary matrices.

A: Given- 2-40013006 To find- Find a matrix B in reduced row echelon form that is row equivalent to A,…

Q: Find ∣A−1∣ for the matrix

A:

Q: Which is the matrix inverse to the matrix 2 3 1 3 2 1 1 0 1

A:

Q: DEMONSTRATE THAT A A-1= A-1A = I      FOR THE MATRIX BELOW     1 -1 2 2 -3 4 1 0 3

A: Given matrix A=1-122-34103 We have to  prove that AA-1=A-1A=I We know that A-1=AdjAA

Q: Given A = 1 1 0 3 Compute 5A *Matrix

A:

Q: 2. Find the elementary row operation that transforms the first matrix into the second, and then find…

A:

Q: Find a QR-decomposition of the matrix -1 1 1 -1 0 1

A: Here,             . Now, we will be finding the QR decomposition of the above matrix A.

Q: The order of the single matrix obtained from 1 1 -1 To 1 23 is 1 0 21 -1 0 2 2 0 3 2 (a) 2 x 3

A: Here the order of the matrix needs to find out for both terms. Subtraction and addition won't affect…

Q: 2. Verify Calay-Hamilton theorem for the following matrix: (2 1 -1 A = (3 1 1 0 2

A: Solution:Given        A=21-1310102To findA-λI=0

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

A:

Q: 2. Let the rref of a matrix A be, 0 2 0 -2 0 1 -5 0 -3 0 0 0 1 6 Determine A if the first, second…

A:

Q: 1 2 3 A = 1 3 2 2 6 8

A: See solution below

Q: 3 (i);- 2

A:

Q: The multiplicative identity matrix of order 2 is I2 =_______.

A:

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

A:

Q: I1,I2,I3 of th

A: Here we have;  11I1+4I2+3I3=-4-15I1+4I2+4I3=163I1+4I2+17I3=3 let;  AX=B  where  A=1143-15443417,…

Q: Find a matrix P that will diagonalize A. Then use it to find A13 in a computationally efficient way.…

A:

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: 1- the rank of the matrix A.

A:

Q: (a) Show that if A is a square matrix with linearly independent columns, then A+ = A -1• (b) If A is…

A:

Q: 2. Find a single matrix equal to [1 - i 1+0, where i = √-1 (imaginary unit).

A: To find the product of the given 3 matrices.

Q: (b) Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, [1 3.…

A: Given :          A = 13-223001-1   To find the inverse of A. Also, to compute 3A-1.

Q: 2. Let the rref of a matrix A be, 1 0 2 0 -2) 0 1 -5 0 -3 0 0 1 6 Determine A if the first, second…

A:

Q: Find an elementary matrix E that corresponds to the row operation of subtracting – 6 times Row 1…

A: Applying elementary row operation on identity matrix I we get the elementary matrix E.Now we find a…

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

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.