Let A = beginpmatrix2 -1 0 2 endpmatrix. If B = I - 5 C 1( operatornameadj A )+ 5 C 2 ( operatornameadj A)2- ldots- 5 C 5( operatornameadj A )5, then the sum of all elements of the matrix B is:

Question

Let A = beginpmatrix2 -1 0 2 endpmatrix. If B = I - 5 C 1( operatornameadj A )+ 5 C 2 ( operatornameadj A)2- ldots- 5 C 5( operatornameadj A )5, then the sum of all elements of the matrix B is: (A) -5 (B) -6 (C) -7 (D) -8

Tardigrade Admin · Accepted Answer

B =( I - operatornameadj A )5=[-1 -1 0 -1]5=[-1 -5 0 -1] Sum of its all elements =-7.

Q. Let $A = (20 - 1 2)$ . If $B = I -^{5} C_{1} (adj A) +^{5} C_{2}$ $(adj A)^{2} - \dots -^{5} C_{5} (adj A)^{5}$ , then the sum of all elements of the matrix $B$ is:

-5

-6

-7

-8

$B = (I - adj A)^{5} = [- 1 0 - 1 - 1]^{5} = [- 1 0 - 5 - 1]$
Sum of its all elements $= - 7$ .

Q. Let A=(20​−12​). If B=I−5C1​(adjA)+5C2​ (adjA)2−…−5C5​(adjA)5, then the sum of all elements of the matrix B is:

-5

-6

-7

-8

B=(I−adjA)5=[−10​−1−1​]5=[−10​−5−1​] Sum of its all elements =−7.

Q. Let $A = (20 - 1 2)$ . If $B = I -^{5} C_{1} (adj A) +^{5} C_{2}$ $(adj A)^{2} - \dots -^{5} C_{5} (adj A)^{5}$ , then the sum of all elements of the matrix $B$ is:

$B = (I - adj A)^{5} = [- 1 0 - 1 - 1]^{5} = [- 1 0 - 5 - 1]$
Sum of its all elements $= - 7$ .