Topic Details (Notes format)

How to Use Matrices for Solving Linear Systems

Subject: Mathematics

Book: Maths Mastery

Matrices transform sets of linear equations into a compact form AX = B, where A holds coefficients, X is the variable matrix, and B is the constants matrix. Techniques like Gaussian elimination or inverse matrices help solve for X. For example, if A is a 2×2 matrix and B is a 2×1 matrix, finding X often involves computing A⁻¹B. Matrices are crucial in computer graphics (transformations), engineering (stress-strain systems), and advanced math modeling. Proficiency ensures you can handle large or complex linear systems systematically, bridging theoretical knowledge with powerful computational methods.

Practice Questions

What is the HCF of 72 and 120?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If x^2 + 4x + 4 = 0, what is the value of x?

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What is the value of x if log(x) + log(4) = log(32)?

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What is the square root of 144?

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If 2a + b = 10 and a - b = 4, what is the value of a?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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