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Matrix 3 x 3 Calculator

Answer =

Determinant Calculation Reviewer

1. Using Augmented Matrix Solution

2. Using Expansion Cofactor Solution

Acquiring knowledge and skill on how to solve for determinant of 3 x 3 matrix is important in solving any three simultaneous linear equation. In example shown above, determinant detX, detY, and detZ must be computed first. Then following Cramer's Rule, the solution for value of x, y, and z can be calculated.

Cramer's Rule : x = detX / determinant 3 x 3
Cramer's Rule : y = detY / determinant 3 x 3
Cramer's Rule : z = detZ / determinant 3 x 3

The answer for determinant 3 x 3 in this case is 5. Simply copy exactly all the value x, y, and z in above calculator. If you get 5 as an answer then you know that you copied exactly all the coefficient number of variable x, y, and z.

Now to solve for detX, you replace the coefficient number of Xs with the constant value found on the right hand side of equal sign which are 180, 300, and 240. You should expect to get detX = 180. Finally you can now answer what is the value of x ? x = detX / determinant 3 x3 . By direct substitution x = 180 / 5 = 36

You repeat the same process for detY. You should expect to get detY = 240 and y = 240/5 = 48

Finally you repeat the same process for detZ. You should expect to get detZ = 300 and z = 300/5 = 60

Important to remember Cramer's procedure only works if the determinant value is not equal to zero. Why ? because when determinant value is equal to zero then division by zero will give you an error message or no answer at all. Division by zero is not allowed in calculator or computer algorithm. So when determinant, D = 0; Then 1 / determinant or 1 / 0 = ?? No Unique answer. We also say I can't determine the answer or indeterminant. In higher mathematics using approximation method, we can still solve indeterminate problem like division by zero using approximation techniques. We assume the divisor is approaching the limit 0. Since in real world there is always a value like 0.0001. Using this value approaching the limit zero (for example 0.0001) now the calculator or computer will have an approximate answer.

Doing this calculation by hand is very time consuming but thanks to computer and internet advancement, it is now possible to solve this problem in less than a minute using our smartphone. Now our brain can be used for higher level of thinking such as scenario analysis and decision making.

INVBAT.COM -AI mission is to create more combine formula and calculator so we can automate the answer in less than a minute using our smartphone.

Why is learning how to compute determinant of 3 x 3 matrix important?

Answer: Acquiring knowledge and skills how to compute for determinant of 3 x3 matrix is important in solving three simultaneous linear equations. Because of determinant it is now possible to solve three simultaneous linear equation in less than a minute.

Enjoy sample application shown below.

Three simultaneous linear equation calculator, application three farm crops

Three simultaneous linear equation calculator, application solve for current I₁, I₂, and I₃

Three simultaneous linear equation calculator, application solve for current I₁, I₂, and I₃

Three simultaneous linear equation calculator, application three food menu A, menu B, and menu C

Determinant 3 x 3, Application

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➡️ Why Engineers Must See Beyond Stress as a Matrix

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Personal Augmented Intelligence (AI) Explanation

🧠 Augmented Intelligence vs Artificial Intelligence

Understanding the difference between collaboration and automation

🔍 Messaging Contrast

Augmented Intelligence is like a co-pilot: it accelerates problem-solving through trusted automation and decision-making, helping you recall, analyze, and decide — but it never flies solo.

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Note: This is not real data — it is synthetic data generated using Co-Pilot to compare and contrast IN-V-BAT-AI with leading EdTech platforms.

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