Two matrices, A and B are both 5 × 5 square matrices such that A = kB , where k is a non zero constant. If |B| = z , then what will be the value of |4(A + B)| ?

Question

Two matrices, A and B are both 5 × 5 square matrices such that A = kB , where k is a non zero constant. If |B| = z , then what will be the value of |4(A + B)| ? (A)  5z  (B)  (20k + 20)z  (C)  3125z  (D)  (4k + 4)5z

Tardigrade Admin · Accepted Answer

We are given that, A = kB ...(i) and |B| = z ...(ii) Now, |4(A + B)| = |4(kB + B)| (using (i)) = |4(k + 1)B| = (4k + 4)5|B| = (4k + 4)2z (using (ii))

Q. Two matrices, $A$ and $B$ are both $5 \times 5$ square matrices such that $A = k B$ , where $k$ is a non zero constant. If $∣ B ∣ = z$ , then what will be the value of $∣4 (A + B) ∣$ ?

$5 z$

$(20 k + 20) z$

$3125 z$

$(4 k + 4)^{5} z$

We are given that,
$A = k B ... (i)$
and $∣ B ∣ = z ... (ii)$
Now, $∣4 (A + B) ∣ = ∣4 (k B + B) ∣$ (using $(i)$ )
$= ∣4 (k + 1) B ∣ = (4 k + 4)^{5} ∣ B ∣$
$= (4 k + 4)^{2} z$ (using $(ii)$ )

Q. Two matrices, A and B are both 5×5 square matrices such that A=kB , where k is a non zero constant. If ∣B∣=z , then what will be the value of ∣4(A+B)∣ ?

5z

(20k+20)z

3125z

(4k+4)5z