Topic Details (Notes format)

How to Multiply Matrices (2x2 and Beyond)

Subject: Mathematics

Book: Maths Mastery

Matrix multiplication is defined by taking the dot product of rows of the first matrix with columns of the second. For a 2×2 example, if A=[[a,b],[c,d]] and B=[[e,f],[g,h]], then A×B=[[ae+bg, af+bh],[ce+dg, cf+dh]]. The process generalizes to larger dimensions where inner dimensions must match. Matrix multiplication underlies transformations in 2D/3D graphics, network flows, Markov chains, or advanced linear systems. Gaining fluency is a key step in linear algebra, enabling big leaps in data analysis and computational problem-solving.

Practice Questions

If 5x - 2 = 13, what is the value of x?

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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The LCM of 12 and 15 is:

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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What is the square root of 121?

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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What is the value of log₃(27)?

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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