1.

(4) Determine the values of a and so that the following matrices are singular:A=(7 3 -2 a)​

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A MATRIX B is said to be SINGULAR if

det B = |B| = 0

Now it is given that

\displaystyle \: A = \displaystyle\begin{pmatrix} \: \: \: 7 & \: 3\\ - 2 & \: a \end{pmatrix}

Now

| A | = \displaystyle\begin{vmatrix} \: \: \: 7 & 3 \\ - 2 & a \end{vmatrix} = (7 \times a) - ( - 2 \times 3) = 7a + 6

Since A is singular

So

\displaystyle \: 7a + 6 = 0

\implies \: a \: = - \frac{6}{7}


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