ECO201_Lec 4_26 May

# ECO201_Lec 4_26 May - ECO201 Lecture 4 Section 1 Matrix...

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Unformatted text preview: ECO201 Lecture 4 Section 1 Matrix Algebra: c1 P1 + c 2 P2 = −c 0 γ 1 P1 + γ 2 P2 = −γ 0 c1 γ 1 c 2 P1 − c 0 P = − γ γ2 2 0 a11 x1 + a12 x 2 + a13 x3 ....... + a1n x n = d 1 a 21 x1 + a 22 x 2 + a 23 x3 ....... + a 2 n x n = d 2 .......................................................... a m1 x1 + a m 2 x 2 + a m 3 x3 ....... + a mn x n = d m a 21 a11 a a 22 21 a m1 a m 2 ( m ×n) a1n x1 d 1 a 2 n x 2 d 2 = a mn x n d m ( n ×1) ( m ×1) Ax = d • Elements of a matrix: aij • A is the coefficient matrix, x and d are known as vectors. A vector can be a row vector or a column vector. Both matrix and vectors have dimensions indicating to the number or rows and columns. For example, (mxn) read ‘m by n’ indicates that there are m rows and n columns. Remember, the row number always precedes the column number. • Square matrix is a matrix that has equal number of rows and columns. 1 3 A= 5 9 4 or B = 9 1 6 5 2 8 3 7 • Matrix operation- Addition, Subtraction and Scalar multiplication • Two matrices A and B can be added with each other if and only if they have the same dimension. This is also true for matrix subtraction. This is known as conformability condition. • We can multiply a matrix by a scalar. A scalar is a numerical element- a number. ...
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ECO201_Lec 4_26 May - ECO201 Lecture 4 Section 1 Matrix...

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