Question

If the matrix a is such that: a = [ 2 4 7 ] [1 9 5] then the determinant of a is equal to:

Answer 1

we cannot do matrix multiplication here because the no of Columns of first matrix is not equal to the no of rows of second matrix

Answer 2

Concept

A matrix is an array or table of numbers, arranged in rows and columns. The determinant of a matrix is the scalar value or number that is calculated using a square matrix. The matrix has to be square, then only a determinant can be calculated.  

Given

a = $\left[\begin{array}{ccc}2\\4\\7\end{array}\right] \left[\begin{array}{ccc}1&9&5\end{array}\right]$

Find

we are asked to find the determinant of 'a'

Solution

we have,

a = $\left[\begin{array}{ccc}2\\4\\7\end{array}\right] \left[\begin{array}{ccc}1&9&5\end{array}\right]$

Multiplying the two matrices, we get-

a = $\left[\begin{array}{ccc}2*1&2*9&2*5\\1*4&4*9&4*5\\7*1&7*9&7*5\end{array}\right]$

a = $\left[\begin{array}{ccc}2&18&10\\4&36&20\\7&63&35\end{array}\right]$

we can write as,

a = 2 * 4 * 7  $\left[\begin{array}{ccc}1&9&5\\1&9&5\\1&9&5\end{array}\right]$

Now, we find the determinant of the 3 * 3 matrix

Here we see that two columns of matrix a are identical

⇒ the determinant of the matrix will be 0

Thus the determinant of a is equal to 0

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