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25. BASIC MATRIX OPERATIONS MATRIX • A matrix is a rectangular array of numbers in rows and columns. 2 3 −1 8 0 1.2 DIMENSIONS • The dimensions of a matrix with m rows and n columns are m X n. 2 3 −1 8 0 1.2 • The matrix has 3 rows and 2 columns so the dimensions are 3 X 2. ELEMENTS • The numbers in a matrix are its elements. 2 3 −1 8 0 1.2 • Elements are identified by their row and column. Thus, element 3,2 is 1.2. EQUAL MATRICES • Equal matrices have the same dimensions and the elements in corresponding positions are equal. SCALAR MULTIPLICATION • In matrix algebra, a real number is often called a scalar. To perform scalar multiplication, you multiply each element in the matrix by the scalar. PROPERTIES OF MATRICES • Associative Property of Addition o(A + B) + C = A + (B + C) • Commutative Property of Addition oA + B = B + A oWe will see tomorrow that matrices do not have the commutative property of multiplication • Distributive Property of Addition/Subtraction ok(A + B) = kA + kB ok(A – B) = kA – kB ADDING AND SUBTRACTING MATRICES • To add or subtract two matrices, simply add or subtract corresponding elements. • You can add or subtract matrices only if they have the same dimensions. TRY THIS! • Perform the indicated operation, if possible. 6 1 −2 3 3 2 −2 0 7 1 1 3 + −2 6 1 −4 9 5 TRY THIS! • Perform the indicated operations, if possible. 0 3 −7 6 2 −1 4 1 −2 3 0 −5 MULTI-STEP PROBLEM • Two pet stores sell both dogs and cats. Sales from each store for last month and this month are shown below: • Organize the data into matrices, then write and interpret a matrix giving the average monthly sales for the two month period. • Last Month: Store 1 sold 42 dogs, 33 cats. Store 2 sold 56 dogs, 21 cats. • This Month: Store 1 sold 36 dogs, 51 cats. Store 2 sold 48 dogs, 37 cats. ONE MORE! • Solve the matrix equation for x and y. −2 1 3 −2𝑥 − −5𝑦 1 7 −6 −4 = 4 8 12 −6 ON YOUR CALCULATOR • Let’s see how to input matrices in the calculator