Download to read offline
![Properties of
Matrices
Dr. Mehar
Chand
Properties of
Matrix
Addition
Commutative Law
Associative Law
Existence of Identity
Existence of Inverse
Cancellation Laws
Scalar
Multiplication
Examples
Video
Properties of Matrix Addition
Definition (Cancellation Laws)
If A, B and C are three matrices of same order, then
A + B = A + C ⇒ B = C [ Left Cancellation Law]
B + A = C + A ⇒ B = C [ Right Cancellation Law]
Dr. Mehar Chand Properties of Matrices](https://image.slidesharecdn.com/tutorial-4-200423234904/75/Tutorial-4-Properties-of-Matrices-Addition-7-2048.jpg)
More Related Content
Similar to Tutorial 4 : Properties of Matrices Addition
Tutorial 4 : Properties of Matrices Addition
- 1. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Tutorial-IV: Matrices Basic Mathematics: Properties of Matrices Dr. Mehar Chand Department of Mathematics Baba Farid College, Bathinda-151001 April 24, 2020 Dr. Mehar Chand Properties of Matrices
- 2. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Contents 1 Properties of Matrix Addition Commutative Law Associative Law Existence of Additive Identity Existence of Additive Inverse Cancellation Laws 2 Properties of Scalar Multiplication 3 Examples 4 Full video Lecture Dr. Mehar Chand Properties of Matrices
- 3. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Properties of Matrix Addition Definition (Commutative Law) If A and B are matrices of order m × n, then A + B = B + A Dr. Mehar Chand Properties of Matrices
- 4. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Properties of Matrix Addition Definition (Associative Law) If A, B and C are matrices of order m × n, then (A + B) + C = A + (B + C) Dr. Mehar Chand Properties of Matrices
- 5. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Properties of Matrix Addition Definition (Existence of Additive Identity) For every Matrix A, there exist a matrix O such that A + O = A = O + A Dr. Mehar Chand Properties of Matrices
- 6. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Properties of Matrix Addition Definition (Existence of Additive Inverse) For every Matrix A, there exist a matrix B such that A + B = O = B + A Dr. Mehar Chand Properties of Matrices
- 7. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Properties of Matrix Addition Definition (Cancellation Laws) If A, B and C are three matrices of same order, then A + B = A + C ⇒ B = C [ Left Cancellation Law] B + A = C + A ⇒ B = C [ Right Cancellation Law] Dr. Mehar Chand Properties of Matrices
- 8. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Properties of Matrix Addition Definition (Properties of Scalar Multiplication) If A and B are matrices of same order and k, l are scalars, then 1 k(A + B) = kA + kB 2 (k + l)A = kA + lA 3 k(lA) = (kl)A 4 (−k)A = −(kA) = k(−A) Dr. Mehar Chand Properties of Matrices
- 9. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Examples Example (1) If A = 1 2 −3 5 0 2 1 −1 1 , B = 3 −1 2 4 2 5 2 0 3 and C = 4 1 2 0 3 2 1 −2 3 , then compute A + B and B − C Also verify that A + (B − C) = (A + B) − C Dr. Mehar Chand Properties of Matrices
- 10. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Examples Example (2) If A = 8 0 4 −2 3 6 and B = 2 −2 4 2 −5 1 , then find the matrix X such that 2A + 3X = 5B Example (3) Find X and Y, If 2X + 3Y = 2 3 4 0 and 3X + 2Y = 2 −2 −1 5 . Dr. Mehar Chand Properties of Matrices
- 11. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Full video Lecture To see full video lecture visit the below link https://youtu.be/hEId2ZuD4Qc Dr. Mehar Chand Properties of Matrices
- 12. Properties of Matrices Dr. Mehar Chand Propertiesof Matrix Addition Commutative Law Associative Law Existence of Identity Existence of Inverse Cancellation Laws Scalar Multiplication Examples Video Thank you Dr. Mehar Chand Properties of Matrices