RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices (Ex 5.3) Exercise 5.3 - Free PDF
Free PDF download of RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices Exercise 5.3 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 5 - Algebra of Matrices Ex 5.3 Questions with Solutions for RD Sharma Class 12 Maths to help you to revise the complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance exams.
FAQs on RD Sharma Class 12 Solutions Chapter 5 - Algebra of Matrices (Ex 5.3) Exercise 5.3
1. What are matrices?
Matrices can be defined as a rectangular array of numbers real or complex. A matrix has m number of rows and n numbers of columns. For the representation of matrices brackets i.e.  or () are used. We can understand this with the example of a row matrix (also called row vector) which consists of a single row. They are written as [a1 a2 a3 ………. an] or [1, 7, 15].
2. How do we add or subtract matrices?
Suppose there are 2 matrices X and Y in the same order. For the addition of these two matrices it can be done by X + Y. Again, for the subtraction of these matrices, you can simply subtract the corresponding elements.
Thus, if X = (xij) m × n and Y = (yij) m × n, then X + Y = (xij + yij) m × n
3. What are the properties of multiplying two matrices?
The properties of multiplication are as follows:
Multiplication of matrix is not commutative that is, XY ≠ YZ.
Multiplication of matrix is associative i.e. (XY) Z = X (YZ)
(X + Y) Z = XZ + YZ and also, X(Y+Z) = XY +XZ
When XY=XZ then Y=Z, if it is an invertible matrix i.e. the matrix, has invertible functions given it satisfies the required conditions.
If there are two non-zero matrices then the product of these two will be non-zero too.
4. Is this chapter important for the IIT JEE exam?
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