Please solve for part a and b. 4. Derive the cofactor expansion formula for determinant by completing the following exercises. Properties I-iii are key properties of the determinant. We can derive other statements about the determinant using these properties. i.The determinant of the identity matrix is 1. ii. Switching two rows changes the sign of the determinant iii. The determinant is a line function in each row (separately).In other words Exercise 4.a: Show that the determinant of a diagonal matrix is the product of diagonal entries using the key properties(10 points) Exercise 4.b:Derive the determinant formula of a 2-by-2 using the key properties (10 points) a11 a12 a21 a22
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a, consider a diagonal matrix D with diagonal entries a11, a22, ..., ann. Show more…
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Hint: In this exercise you have to use the following property: if a matrix V is obtained from a matrix U by multiplying 1 row or 1 column of U by a scalar k, then det(V) = k det(U). Let M be the matrix Complete the following: a) The determinant of M can be expressed as 5det A, where A is the 3*3 matrix defined as (Matrix A to be completed). b) The determinant of A can be expressed as 3det B,where B is the 2*2 matrix defined as (Matrix B to be completed) c) The determinant of B is d) Thus the determinant of M is
Adi S.
Compute the determinant of the matrix A, below, by using row operations to transform A to an upper-triangular matrix B. Then express the determinant of A as a multiple k of the determinant of B, and use this to compute the determinant of A. A = [ 0 -35 -4 -19 ] [ 0 7 0 3 ] [ 0 0 1 -1 ] [ 10 7 -1 -4 ] B = [ 0 0 0 ] [ 0 0 0 ] [ 0 0 0 ] det(A) = k·det(B)
Vincenzo Z.
Properties of determinants: The determinant is defined by det I = 1, sign reversal, linearity in each row. After elimination with no row exchanges det A = (product of the pivots). det AB = (det A) (det B) det AT = det A 1. If A is a 3 x 3 matrix with det A = 1/2, find (a) det 2A (b) det A^2 (c) det A^-1 2. Find the determinant of the matrix (a) A = (1 2 5; 0 3 -9; 0 0 2) (b) A = (1 2 5; 0 3 -9; 1 5 -2) (c) A = (5 0 1 0; 6 2 0 0; -2 0 1 -4; 1 0 1 0) 3. Vandermonde determinant. Start with elimination performed on the first column followed by the cofactor method to evaluate V3 = det (1 a a^2; 1 b b^2; 1 c c^2)
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