Which of following is correct?

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3 and 4 .Determinants and Matrices

easy

Which of the following is correct?

Determinant is a square matrix.

Determinant is a number associated to a matrix.

None of these.

Determinant is a number associated to a square matrix.

Solution

We know that to every square matrix, $A=[\text { aij }]$ of order $n .$ We can associate a number called the determinant of square matrix $A$, where $a i j=(i, j)^{\text {th }}$ element of $A$.

Thus, the determinant is a number associated to a square matrix.

Hence, the correct answer is $D$.

Standard 12

Mathematics

Let $A =$ $\left[ {\begin{array}{*{20}{c}}{1 + {x^2} – {y^2} – {z^2}}&{2(xy + z)}&{2(zx – y)}\\{2(xy – z)}&{1 + {y^2} – {z^2} – {x^2}}&{2(yz + x)}\\{2(zx + y)}&{2(yz – x)}&{1 + {z^2} – {x^2} – {y^2}}\end{array}} \right]$ then det. $A$ is equal to

normal

$\left| {\,\begin{array}{*{20}{c}}{{{\sin }^2}x}&{{{\cos }^2}x}&1\\{{{\cos }^2}x}&{{{\sin }^2}x}&1\\{ – 10}&{12}&2\end{array}\,} \right| = $

easy

$\left| {\,\begin{array}{*{20}{c}}{19}&{17}&{15}\\9&8&7\\1&1&1\end{array}\,} \right| = $

easy

For how many diff erent values of $a$ does the following system have at least two distinct solutions?

$a x+y=0$

$x+(a+10) y=0$

medium

(KVPY-2017)

Let the system of linear equations $x +2 y + z =2$, $\alpha x +3 y – z =\alpha,-\alpha x + y +2 z =-\alpha$ be inconsistent. Then $\alpha$ is equal to

medium

(JEE MAIN-2022)

Which of the following is correct?

Solution

Similar Questions

Let $A =$ $\left[ {\begin{array}{*{20}{c}}{1 + {x^2} – {y^2} – {z^2}}&{2(xy + z)}&{2(zx – y)}\\{2(xy – z)}&{1 + {y^2} – {z^2} – {x^2}}&{2(yz + x)}\\{2(zx + y)}&{2(yz – x)}&{1 + {z^2} – {x^2} – {y^2}}\end{array}} \right]$ then det. $A$ is equal to

$\left| {\,\begin{array}{*{20}{c}}{{{\sin }^2}x}&{{{\cos }^2}x}&1\\{{{\cos }^2}x}&{{{\sin }^2}x}&1\\{ – 10}&{12}&2\end{array}\,} \right| = $

$\left| {\,\begin{array}{*{20}{c}}{19}&{17}&{15}\\9&8&7\\1&1&1\end{array}\,} \right| = $

For how many diff erent values of $a$ does the following system have at least two distinct solutions? $a x+y=0$ $x+(a+10) y=0$

Let the system of linear equations $x +2 y + z =2$, $\alpha x +3 y – z =\alpha,-\alpha x + y +2 z =-\alpha$ be inconsistent. Then $\alpha$ is equal to

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For how many diff erent values of $a$ does the following system have at least two distinct solutions?

$a x+y=0$

$x+(a+10) y=0$