Scalar Multiplication Of Matrices Worksheet Worksheet by Kuta Software LLC Math IV Matrix Addition Subtraction Scalar Multiplication Name ID 1 Date Period h2B0P1Q5S xKsuztoaS GSko fftYwfarrHeA PLHLHCf v j zAIlHlf MrSiRgthxtOs Irneys e rOvheHd 1 Simplify Write undefined for expressions that are undefined
K A B kA kB Scalar Multiplication Distributive Property kA Ak A 0 0 A A Additive Identity 0A 0 Be sure that this last property makes sense it says that if we multiply any matrix by the number 0 the result is the zero matrix or 0 We began this section with the concept of matrix equality The term scalar multiplication refers to the product of a real number and a matrix In scalar multiplication each entry in the matrix is multiplied by the given scalar For example given that A 10 6 4 3 let s find 2 A To find 2 A simply multiply each matrix entry by 2 2 A 2 10 6 4 3 2 10 2 6 2 4 2 3
Scalar Multiplication Of Matrices Worksheet
Scalar Multiplication Of Matrices Worksheet
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Matrix Multiplication
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Apply scalar multiplication as part of the overall simplification process Example 1 Perform the indicated operation for latex 2A latex I will take the scalar 2 similar to the coefficient of a term and distribute it by multiplying it to each entry of matrix latex A latex In case you forgot you may review the general formula above ID 1403636 17 09 2021 Country code TT Country Trinidad Tobago School subject Math 1061955 Main content Scalar multiplication of matrices 1527271 Scalar multiplication of matrices with addition and subtraction of matrices included Other contents Addition and Subtraction of Matrices
Associative property of multiplication c d A c d A This property states that if a matrix is multiplied by two scalars you can multiply the scalars together first and then multiply by the matrix Or you can multiply the matrix by one scalar and then the resulting matrix by the other The following example illustrates this property Is a 2 2 matrix B is 3 2 C is 2 3 and D is 3 2 From these four matrices only B and D are compatible This means we can calculate B D B D D B but we cannot add or subtract any other pair of these matrices 3 The matrix CT 0 2 matrix so we could add or subtract CT to from B and D 3
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Do 4 problems Learn for free about math art computer programming economics physics chemistry biology medicine finance history and more Khan Academy is a nonprofit with the mission of providing a free world class education for anyone anywhere 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 1 Try the following matrix operations a 3 1 0 0 1 b 1 1 1 1 0 1 1 0 c 1 2 2 4 2 1 3 0 d
Matrix Multiplication Date Period Simplify Write undefined for expressions that are undefined 1 0 2 2 5 6 6 3 0 6 0 27 12 2 6 3 5 4 Create your own worksheets like this one with Infinite Algebra 2 Free trial available at KutaSoftware Title Matrix Multiplication Examples solutions videos worksheets games and activities to help Algebra students learn about matrix addition subtraction and scalar multiplication Properties of Matrices Adding and subtracting matrices as well as scalar multiplication Matrix Operations Adding Subtracting and Multiplying by a constant for matrices is discussed
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Scalar Multiplication Of Matrices Worksheet - 14 Matrix Addition and Scalar Multiplication For matrices a similar property holds That is if A is an m n matrix and O is the m n zero matrix consisting entirely of zeros then A O A In other words O is the additive identity for the set of all m n matrices For example the following matrices are the