A matrix is Singular if its determinant is zero otherwise it is called as non-singular matrix, so now try some practice questions.
Check which of the following matrices are Singular or Non-Singular.
1). \(\begin{bmatrix}1 & -1 &0 \\4 &5 &5 \\ 1& 5 &6 \end{bmatrix}\)
2). \(\begin{bmatrix}5 & 4 &0 \\5 &0 &0 \\ 5& 5 &0 \end{bmatrix}\)
3). \(\begin{bmatrix}1 & 2 &3 \\-1 &7 &1 \\ 2& 4 &6 \end{bmatrix}\)
4). \(\begin{bmatrix}-2 & 1 &1 \\6 &3 &-3 \\ 4& 9 &-2 \end{bmatrix}\)
5). \(\begin{bmatrix}2 & -3 &0 \\0 &5 &5 \\ 0& 0 &6 \end{bmatrix}\)
6). \(\begin{bmatrix}12 & 8 &0 \\0 &0 &5 \\ 0& 0 &6 \end{bmatrix}\)
7). \(\begin{bmatrix}1 & 8 & \frac{1}{3} \\3 &5 &\frac{1}{9} \\ 8& 0 &\frac{1}{24} \end{bmatrix}\)
Answers :
1). Non-Singular
2). Singular
3). Singular
4). Singular
5). Non-Singular
6). Singular
7). Singular
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