If $|A| = 13$ and $|\text{Adj } A| = \begin{vmatrix} 4 & x \\ 5 & 7 \end{vmatrix}$, then the value of $x$ is : (a) $3$ (b) $4$ (c) $2$ (d) $-5$

If |A| = 13 and |Adj A| = 4 x \5 7 , then the value of x is : (a) 3 (b) 4 (c) 2 (d) -5

Question 12 of 44

|A| = 13

(a)

3

(b)

4

(c)

2

(d)

-5

Puducherry TnboardTamil Nadu HSC (DGE) Commerce Board 2020MCQ· 1mImportance★★★★★

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Use $|\text{Adj }A| = |A|^{n-1}$ with $n = 2$ , so $|\text{Adj }A| = |A| = 13$ ; then equate the given determinant to $13$ and solve for $x$ . This is a very common TN HSC Class-12 Business Mathematics matrices-and-determinants question.

Step 1 — Apply the adjoint property.

For a square matrix $A$ of order $n$ , $\;|\text{Adj }A| = |A|^{\,n-1}$ .

The adjoint here is a $2\times 2$ determinant, so $A$ is of order $n = 2$ :

$|\text{Adj }A| = |A|^{\,2-1} = |A|^{1} = |A| = 13.$

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Q.If $|A| = 13$ and $|\text{Adj } A| = \begin{vmatrix} 4 & x \\ 5 & 7 \end{vmatrix}$ , then the value of $x$ is :

Concept understanding — Rank of a Matrix

Rank of a Matrix

Q.If ∣A∣=13|A| = 13∣A∣=13 and ∣Adj A∣=∣4x57∣|\text{Adj } A| = \begin{vmatrix} 4 & x \\ 5 & 7 \end{vmatrix}∣Adj A∣=​45​x7​​, then the value of xxx is :

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Q.If $|A| = 13$ and $|\text{Adj } A| = \begin{vmatrix} 4 & x \\ 5 & 7 \end{vmatrix}$ , then the value of $x$ is :

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