By Ernst Neufert
This e-book was once asked by way of our layout and Drafting Chair and he's tremendous proud of the content material.
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Additional info for Architects' Data (3rd Edition)
If |A| = 0. The rows and columns of a nonsingular matrix are linearly independent in the sense that no row (or column) is a linear combination of other rows (or columns). If the coefﬁcient matrix is singular, the equations may have an inﬁnite number of solutions, or no solutions at all, depending on the constant vector. As an illustration, take the equations 2x + y = 3 4x + 2y = 6 Since the second equation can be obtained by multiplying the ﬁrst equation by two, any combination of x and y that satisﬁes the ﬁrst equation is also a solution of the 30 Systems of Linear Algebraic Equations second equation.
Ak j .. Ai j .. Anj ··· ··· ··· ··· ··· ··· A1n A2n A3n .. Akn .. Ain .. Ann ⎤ b1 b2 ⎥ ⎥ ⎥ b3 ⎥ ⎥ .. ⎥ ⎥ ⎥ bk ⎥ ← pivot row ⎥ .. ⎥ ⎥ bi ⎥ ⎥ ← row being transformed .. ⎦ bn Let the ith row be a typical row below the pivot equation that is to be transformed, meaning that the element Aik is to be eliminated. We can achieve this by multiplying the pivot row by λ = Aik/Akk and subtracting it from the ith row. The corresponding changes in the ith row are Ai j ← Ai j − λAk j , j = k, k + 1, . .
If x is a matrix, then a is a row vector containing the products over each column. For example, >> a = [1 2 3 4 5 6]; >> A = reshape(a,2,3) A = 1 3 5 2 4 6 12 30 >> prod(a) ans = 720 >> prod(A) ans = 2 sum a = sum(x) This function is similar to prod, except that it returns the sum of the elements. 8 Writing and Running Programs cross c = cross(a,b) The function cross computes the cross product: c = a × b, where vectors a and b must be of length 3. 8 Writing and Running Programs MATLAB has two windows available for typing program lines: the command window and the editor/debugger.