Matrix Q/A; Matrix Determinant Problem: Solving for a and b When a = b

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Hello amazing people! It’s another beautiful moment with Mathematics, and today I’m excited to walk you through a matrix problem. In this particular question, we are asked to solve for the variables a and b in a 2x2 matrix with the elements: a, 2, 3, and b, given that the values of both variables (a and b) are equal.

To begin solving this problem, the first step is to find the determinant of the 2x2 matrix and set it equal to 10, as provided in the question. After calculating the determinant and simplifying, we arrive at the equation ab = 16.

However, the goal is to find individual values for either a or b, not their product. So, we apply the condition already stated in the question: a = b. By substituting a in place of b, the equation becomes a² = 16.

From here, we take the square root of both sides of the equation, which gives us a = ±4. Since a = b, it means b is also equal to ±4.

See the clear workings below;

Thanks for visiting my blog and I hope this is helpful.

Tools Used

Graphics tablet/Pen
Miro online white board
Laptop

Video edited with VSDC

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