<p>Name Date: ______Block Math III.Introduction to Matrices</p><p>A matrix is a rectangular arrangement of numbers in ______and ______. </p><p>The dimensions of the matrix are read in order as ______by ______.</p><p>If two matrices have the same dimensions and the same entries (called elements) in corresponding positions, then those matrices are said to be ______.</p><p>Create your own example of equal matrices here:</p><p>Matrices Operations Two or more matrices can be added or subtracted only if they have the same ______. To add or subtract matrices, simply add or subtract the ______.</p><p>In matrix Algebra, a real number is called a ______. To multiply a matrix by a scalar, multiply </p><p>______in the matrix by the scalar. This process is called scalar multiplication. 1 4  3 Find the product o:f   . 2 7 2 </p><p>Note: Matrix operations follow the order of operations rules. Perform the indicated operations. 1  1  7 3  1. 2 2      5 1  3 4 </p><p>1 骣轾4 5 1 轾- 2 3 - 5 2. 琪犏- 犏 = 2 桫臌7 4 2 臌 5- 1 - 12</p><p>To solve a matrix equation: 1. Simplify one or both sides of the equation using matrix operations as needed.</p><p>2. Set ______equal to each other and solve for the variable.</p><p>Solve for x and y:</p><p>01a11221753170a7b23c52fdb245fc14.doc 5/7/2018 轾6 5 轾 6 5 犏 犏 犏x+8 4= 犏 14 - x 4 臌犏0 2y- 1 臌犏 0 - 13 - y</p><p>The seniors are planning a trip for Spring Break. They have contacted three lodges in the vicinity to inquire about rates. They found that Rainbow Lodge charges $13.00 per person per day for lodging, $20.00 per day for food, and $5.00 per person for use of the recreational facilities. Rivers Lodge charges $12.50 for lodging, </p><p>$19.50 for meals, and $7.50 for use of the recreational facilities. Wolf Lodge charges $20.00 per night for lodging, $18.00 per day for meals, and no extra charge for using the recreational facilities. Trout Lodge charges a flat rate of $40.00 per day for lodging (meals included) and no additional fee for use of the recreational facilities. a. Display this information in a matrix, C. The rows and columns have been labeled for you.</p><p>Lodging Food Recreation Rainbow Lodge</p><p>Rivers Lodge</p><p>Wolf Lodge</p><p>Trout Lodge</p><p> b. State the values of C21 and C43.</p><p> c. Interpret C13 and C31.</p><p>Let A, B, and C be matrices and k be a scalar.</p><p>Properties of Matrix Addition Associative Property of Matrix Addition (A + B) + C = ______</p><p>Commutative Property of Addition A + B = ______</p><p>Distributive Property of Addition k(A + B) = ______</p><p>01a11221753170a7b23c52fdb245fc14.doc 5/7/2018 Distributive Property of Subtraction k(A - B) = ______</p><p>Multiplying Matrices</p><p>In order to multiply matrices A X B, the number of ______in A must equal the number of </p><p>______in B. If the product is defined, the solution matrix will have the same number of ______as A, and the same number of ______as B. </p><p>State whether the product is defined. 1. A: 3 X 2; B: 4 X 3 AB? BA?</p><p>2. A: 3 X 3; B: 3 X 2 AB? BA?</p><p>In order to find the product of two matrices, A X B, multiply the rows in A times the columns in B.</p><p>轾6 2 轾-1 2 犏-1 3 3. A = 犏 B = 犏 , find AB. 臌5- 2 臌犏0- 4</p><p>轾4 4. A = [7 3] B = 犏 , find AB and BA. 臌-1</p><p>轾4- 3 轾1 7 轾3- 5 - 2 5. A = 犏 B = 犏 C = 犏 , find (A+B)C. Also find AC +BC. 臌-1 2 臌-4 - 2 臌1 0 6</p><p>Let A, B, and C be matrices and k be a scalar.</p><p>Properties of Matrix Multiplication Associative Property of Matrix Multiplication A(BC) = ______</p><p>Left Distributive Property A(B+C) = ______</p><p>Right Distributive Property (A+B)C = ______</p><p>Associative Property of Scalar Multiplication k(AB) = ______= ______</p><p>01a11221753170a7b23c52fdb245fc14.doc 5/7/2018 NOTE: There is NO Commutative Property of Multiplication for Matrices; generally ______.</p><p>01a11221753170a7b23c52fdb245fc14.doc 5/7/2018</p>