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Definition of a Determinant

If a a ...

Question

If $∣ ∣ ∣ ∣ \begin{matrix} a & a & x m & m & m b & x & b \end{matrix} ∣ ∣ ∣ ∣ = 0$ then $x = ?$

A

a

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B

b

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C

a or b

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D

0

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Solution

The correct option is D a or b
Determinant of a matrix is zero if 2 rows or columns are same.
Hence, if $x = a$ we get $1^{s t}$ and $3^{r d}$ column same
Also, if $x = b$ we get $1^{s t}$ and $2^{n d}$ column same.

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∣ ∣ ∣ ∣ \begin{matrix} a & a & x m & m & m b & x & b \end{matrix} ∣ ∣ ∣ ∣ = 0

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∣ ∣ ∣ ∣ \begin{matrix} a & a & x m & m & m b & x & b \end{matrix} ∣ ∣ ∣ ∣ = 0

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may be equal to

Q. Assertion :Let

A = [\begin{matrix} a & b b & a \end{matrix}]

B = [\begin{matrix} p & q r & s \end{matrix}]

b = 0

A B = B A

b \neq 0

A B = B A

\Leftrightarrow

p = s a n d q = r

.

Q. The solution set of

∣ ∣ ∣ ∣ \begin{matrix} a & a & x m & m & m b & x & b \end{matrix} ∣ ∣ ∣ ∣ = 0

If $\frac{1}{a b^{'}} + \frac{1}{b a^{'}}$ = 0, then lines $\frac{x}{b^{'}} + \frac{y}{a^{'}}$ and $\frac{x}{a} + \frac{y}{b}$ = 1 are ___________________

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