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Matrix Operations The Punch Line Various operations combining linear transformations can be realized with some standard matrix operations Addition and Scalar Multiplication Just like with vector operations the sum of matrices and the multiplica tion by a scalar just a number as opposed to a vector or matrix are done component by component
The 2 2 matrix C represents a rotation by 90 anticlockwise about the origin O followed by a reflection about the straight line with equation y x b Find the elements of C c Describe geometrically the transformation represented by C 0 1 0 A B 0 1
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Worksheet On Matrix Multiplication Multiplication Of Matrices Answers
Worksheet On Matrix Multiplication Multiplication Of Matrices Answers
Part 1 MATRICES AND LINEAR EQUATIONS 1 Chapter 1 SYSTEMS OF LINEAR EQUATIONS3 1 1 Background 3 1 2 Exercises 4 1 3 Problems 7 1 4 Answers to Odd Numbered Exercises8 Chapter 2 ARITHMETIC OF MATRICES9 2 1 Background 9 2 2 Exercises 10 2 3 Problems 12 2 4 Answers to Odd Numbered Exercises14 Chapter
1 Given the matrices A 1 2 3 4 B 0 1 1 1 0 1 compute the following expressions B AB B BA BTB BBT 2I 2 Here I 2is the 2 2 identity matrix If an expression is unde ned explain why Answer B BAis unde ned since the product BAis unde ned Bhas 3 columns while Ahas only two rows Next B AB 2 2 4 5 3 8 BTB 2 4 0 1
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15 Give an example of a matrix expression in which you would first perform a matrix subtraction and then a matrix multiplication Use any numbers and dimensions you would like but be sure that your expression isn t undefined 16 A B and C are matrices A B C AB CA A Always true B Sometimes true C False 2
Name Level 2 Further Maths Ensure you have Pencil or pen Guidance 1 Read each question carefully before you begin answering it 2 Check your answers seem right
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The 2 2 matrix C represents a rotation by 90 anticlockwise about the origin O followed by a reflection about the straight line with equation y x b Find the elements of C c Describe geometrically the transformation represented by C 0 1 0 A B 0 1
https:// math.berkeley.edu /~pglutz/10Bsp18/disc20sol.pdf
Solution There are many possible answers here We just need two matrices so that the number of columns of the rst matrix is not equal to the number of rows in the second One example is 2 6 6 4 1 1 1 0 0 1 0 0 3 7 7 5and 2 4 1 1 3 1 0 4 0 1 5 3 5 e Write two matrices that you can multiply in one order but not in the other order
The 2 2 matrix C represents a rotation by 90 anticlockwise about the origin O followed by a reflection about the straight line with equation y x b Find the elements of C c Describe geometrically the transformation represented by C 0 1 0 A B 0 1
Solution There are many possible answers here We just need two matrices so that the number of columns of the rst matrix is not equal to the number of rows in the second One example is 2 6 6 4 1 1 1 0 0 1 0 0 3 7 7 5and 2 4 1 1 3 1 0 4 0 1 5 3 5 e Write two matrices that you can multiply in one order but not in the other order
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Print The Free Matrix Operations Algebra 2 Worksheet Printable Version
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