EasyMathematicsHigh School (11–12)Algebra › Matrices and DeterminantsNumericalBoard Exam

Find a and b so that 1, 2a, 3; 8, 4, b + 1; 3, 7, 6 is symmetric.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Find $a$ and $b$ so that $

\displaystyle \begin{bmatrix} 1 & 2a & 3 \\ 8 & 4 & b + 1 \\ 3 & 7 & 6 \end{bmatrix}

$ is symmetric.

Need a reminder? The key ideaShow

$(AB)^T = B^TA^T$ . A matrix is symmetric if $A^T = A$ and skew-symmetric if $A^T = -A$ . Every square matrix is $\tfrac{1}{2}(A + A^T) + \tfrac{1}{2}(A - A^T)$ , a symmetric part plus a skew-symmetric part.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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