Determinant of 3x3 matrix
[DOC File]Vectors and Matrices
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The determinant of transposed matrix is the same as the determinant of the original matrix: Det(AT) = Det(A). If we apply the column expansion of equation [44] to an upper triangular matrix, A, we find that Det A = a11A11, since the a11 term is the only term in the first column. We can apply equation [44] repeatedly to the cofactors.
[DOC File]Determinants & Cramer’s Rule
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Evaluate the determinant of a 2x2 and 3x3 matrix. Apply using determinants toward solving 2x2 and 3x3 systems of equations. Calculating the Determinant. Example #1 Practice Problems Calculate the determinant of the matrix. 1. 2. 3. Example #2 Practice Problems Calculate the determinant of the matrix. 4. 5. Cramer’s Rule (for 2x2)
[DOC File]MATRICES
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Co-factor Cij = determinant of 2X2 matrix obtained by deleting row i and column j of A, prefixed by + or – according to following pattern… e.g. C23 is co-factor associated with a23, in row 2 and column 3. so delete row 2 and column 3 to give a 2X2 matrix. co-factor C23 is – determinant of 2X2 matrix (negative sign in position a23)
[DOC File]Department of Mathematics, Texas A&M University
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Finding Determinant of 3x3 Matrix ~ Expansion by Minors (This is the expansion by the first row.) To set-up the minor matrix, ignore the row and column that contains the coefficient. Ex. 2: Find the determinant using expansion by minors: Finding Determinant of 3x3 Matrix ~ Diagonals Method. Ex. 3. Find the determinant for the matrix in example ...
[DOC File]Guide 10: Matrices
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Find the determinant of the following 3x3 matrix: Task Two. Find the determinant of the following 4x4 matrix: Transposing and Inverting a Matrix and Matrix Determinants - ANSWERS. ACTIVITY ONE. Task One. An average is found by adding up a series of numbers and dividing by the number that they are. So for the series above there are twelve ...
[DOC File]Matrices and Determinants
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5. If all elements are real, the matrix is called a real matrix. 6. is called a square matrix of order n. And is called the principal diagonal. e.g. is a square matrix of order 2. 7. Notation : 8.2 Some Special Matrix. Def.8.1 If all the elements are zero, the matrix is called a zero matrix or null matrix, denoted by .
[DOCX File]Matrices 2
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The cross product of (a,c,0) and (b,d,0) is found by taking determinant of 3x3 matrix with rows (i, j, k); (a, c, 0); (b, d, 0). This gives vector 0. i +0. j + (ad-bc) k, whose length is (ad-bc). This length is the area of the parallelogram. So the original unit square gets mapped into a parallelogram with area = ad-bc = det
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