Determinants and their Properties
Matrix and Determinant

79107 If \(A=\left|\begin{array}{lll}4 & k & k \\ 0 & k & k \\ 0 & 0 & k\end{array}\right|\) and \(\operatorname{det}(A)=256\), then \(|k|\)
equals

1 4
2 5
3 6
4 7
5 8
Matrix and Determinant

79108 If \(\left|\begin{array}{ccc}3 i & -9 i & 1 \\ 2 & 9 i & -1 \\ 10 & 9 & i\end{array}\right|=x+i y\), then

1 \(x=1, y=1\)
2 \(x=0, y=1\)
3 \(\mathrm{x}=1, \mathrm{y}=0\)
4 \(x=0, y=0\)
5 \(\mathrm{x}=-1, \mathrm{y}=0\)
Matrix and Determinant

79109 If \(\left(\begin{array}{lll}1 & 2 & 4 \\ 1 & 3 & 5 \\ 1 & 4 & a\end{array}\right)\) is singular, then the value of \(a\) is

1 \(a=-6\)
2 \(a=5\)
3 \(a=-5\)
4 \(a=6\)
5 \(a=0\)
Matrix and Determinant

79110 \(\left|\begin{array}{ccc}1 & 1 & 1 \\ p & q & r \\ p & q & r+1\end{array}\right|\) is equal to

1 \(q-p\)
2 \(q+p\)
3 \(q\)
4 \(\mathrm{p}\)
5 0
Matrix and Determinant

79107 If \(A=\left|\begin{array}{lll}4 & k & k \\ 0 & k & k \\ 0 & 0 & k\end{array}\right|\) and \(\operatorname{det}(A)=256\), then \(|k|\)
equals

1 4
2 5
3 6
4 7
5 8
Matrix and Determinant

79108 If \(\left|\begin{array}{ccc}3 i & -9 i & 1 \\ 2 & 9 i & -1 \\ 10 & 9 & i\end{array}\right|=x+i y\), then

1 \(x=1, y=1\)
2 \(x=0, y=1\)
3 \(\mathrm{x}=1, \mathrm{y}=0\)
4 \(x=0, y=0\)
5 \(\mathrm{x}=-1, \mathrm{y}=0\)
Matrix and Determinant

79109 If \(\left(\begin{array}{lll}1 & 2 & 4 \\ 1 & 3 & 5 \\ 1 & 4 & a\end{array}\right)\) is singular, then the value of \(a\) is

1 \(a=-6\)
2 \(a=5\)
3 \(a=-5\)
4 \(a=6\)
5 \(a=0\)
Matrix and Determinant

79110 \(\left|\begin{array}{ccc}1 & 1 & 1 \\ p & q & r \\ p & q & r+1\end{array}\right|\) is equal to

1 \(q-p\)
2 \(q+p\)
3 \(q\)
4 \(\mathrm{p}\)
5 0
Matrix and Determinant

79107 If \(A=\left|\begin{array}{lll}4 & k & k \\ 0 & k & k \\ 0 & 0 & k\end{array}\right|\) and \(\operatorname{det}(A)=256\), then \(|k|\)
equals

1 4
2 5
3 6
4 7
5 8
Matrix and Determinant

79108 If \(\left|\begin{array}{ccc}3 i & -9 i & 1 \\ 2 & 9 i & -1 \\ 10 & 9 & i\end{array}\right|=x+i y\), then

1 \(x=1, y=1\)
2 \(x=0, y=1\)
3 \(\mathrm{x}=1, \mathrm{y}=0\)
4 \(x=0, y=0\)
5 \(\mathrm{x}=-1, \mathrm{y}=0\)
Matrix and Determinant

79109 If \(\left(\begin{array}{lll}1 & 2 & 4 \\ 1 & 3 & 5 \\ 1 & 4 & a\end{array}\right)\) is singular, then the value of \(a\) is

1 \(a=-6\)
2 \(a=5\)
3 \(a=-5\)
4 \(a=6\)
5 \(a=0\)
Matrix and Determinant

79110 \(\left|\begin{array}{ccc}1 & 1 & 1 \\ p & q & r \\ p & q & r+1\end{array}\right|\) is equal to

1 \(q-p\)
2 \(q+p\)
3 \(q\)
4 \(\mathrm{p}\)
5 0
Matrix and Determinant

79107 If \(A=\left|\begin{array}{lll}4 & k & k \\ 0 & k & k \\ 0 & 0 & k\end{array}\right|\) and \(\operatorname{det}(A)=256\), then \(|k|\)
equals

1 4
2 5
3 6
4 7
5 8
Matrix and Determinant

79108 If \(\left|\begin{array}{ccc}3 i & -9 i & 1 \\ 2 & 9 i & -1 \\ 10 & 9 & i\end{array}\right|=x+i y\), then

1 \(x=1, y=1\)
2 \(x=0, y=1\)
3 \(\mathrm{x}=1, \mathrm{y}=0\)
4 \(x=0, y=0\)
5 \(\mathrm{x}=-1, \mathrm{y}=0\)
Matrix and Determinant

79109 If \(\left(\begin{array}{lll}1 & 2 & 4 \\ 1 & 3 & 5 \\ 1 & 4 & a\end{array}\right)\) is singular, then the value of \(a\) is

1 \(a=-6\)
2 \(a=5\)
3 \(a=-5\)
4 \(a=6\)
5 \(a=0\)
Matrix and Determinant

79110 \(\left|\begin{array}{ccc}1 & 1 & 1 \\ p & q & r \\ p & q & r+1\end{array}\right|\) is equal to

1 \(q-p\)
2 \(q+p\)
3 \(q\)
4 \(\mathrm{p}\)
5 0