Stitz-Zeager_College_Algebra_e-book

# Labeling r3 s and r6 t we have r1 07s 17 r2 35s

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Unformatted text preview: ly, we have j counts columns from left to right A= − − − − − − −→ − − − − − − − − a11 a12 · · · a1n a21 a22 · · · a2n . . . . . . . . . am1 am2 · · · amn i counts rows from top to bottom With this new notation we can deﬁne what it means for two matrices to be equal. Definition 8.6. Matrix Equality: Two matrices are said to be equal if they are the same size and their corresponding entries are equal. More speciﬁcally, if A = [aij ]m×n and B = [bij ]p×r , we write A = B provided 1. m = p and n = r 2. aij = bij for all 1 ≤ i ≤ m and all 1 ≤ j ≤ n. Essentially, two matrices are equal if they are the same size and they have the same numbers in the same spots.2 For example, the two 2 × 3 matrices below are, despite appearances, equal. 0 −2 9 25 117 −3 = √ 3 ln(1) −8 e2 ln(3) 2/3 32 · 13 log(0.001) 125 Now that we have an agreed upon understanding of what it means for two matrices to equal each other, we may begin deﬁning arithmetic operations on matrices. Our ﬁrst operation is addition. Definition 8.7. Matrix Addition: Give...
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