Let A - 1 2- 3 -5 - and B - - 1 0- 0 2 - and X be a matrix such that A - BX- Then -4 - sum of diagonal entries of X is-

The correct option is D 6Let X = [ a amp; b; c amp; d ] ∴[ 1 amp; 2; 3 amp; 5 ] = nbsp;[ 1 amp; 0; 0 amp; 2 ] n ...

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Byju's Answer

Standard XII

Mathematics

Inverse of a Matrix

Let A [ 1 2...

Question

Let $A [\begin{matrix} 1 & 2 3 & - 5 \end{matrix}]$ and $B = [\begin{matrix} 1 & 0 0 & 2 \end{matrix}]$ and X be a matrix such that $A = B X .$ Then $- 4 \times$ sum of diagonal entries of $X$ is,

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Solution

The correct option is D 6
Let $X = [\begin{matrix} a & b c & d \end{matrix}]$
$∴ [\begin{matrix} 1 & 2 3 & - 5 \end{matrix}] = [\begin{matrix} 1 & 0 0 & 2 \end{matrix}] [\begin{matrix} a & b c & d \end{matrix}] = [\begin{matrix} a & b 2 c & 2 d \end{matrix}]$
$∴ a = 1, b = 2, 2 c = 3, 2 d = - 5$
$∴ X = [\begin{matrix} 1 & 2 3 / 2 & - 5 / 2 \end{matrix}] = \frac{1}{2} [\begin{matrix} 2 & 4 3 & - 5 \end{matrix}]$
$- 4 \times$ sum of diagonal entries $= 6$

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Similar questions

Q. Let

A = [\begin{matrix} 1 & 2 \\ 3 & - 5 \end{matrix}] and B = [\begin{matrix} 1 & 0 \\ 0 & 2 \end{matrix}]

and X be a matrix such that A = BX, then X is equal to

(a)

\frac{1}{2} [\begin{matrix} 2 & 4 \\ 3 & - 5 \end{matrix}]

(b)

\frac{1}{2} [\begin{matrix} - 2 & 4 \\ 3 & 5 \end{matrix}]

(c)

[\begin{matrix} 2 & 4 \\ 3 & - 5 \end{matrix}]

(d) none of these.

Q. Assertion :Let

A

be a

2 \times 2

matrix with real entries. Let

I

be the

2 \times 2

identity matrix. Denote by

t r (A)

, the sum of diagonal entries of

A

. Assume that

A^{2} = I

A \neq I

and

A \neq - I

, then

d e t (A) = - 1

Reason: If

A \neq I

and

A \neq - I

, then

t r (A) \neq 0

Q. Let

A

be a

2 \times 2

matrix with real entries, Let I be the

2 \times 2

identity matrix. Denote by

t r (A),

the sum of diagonal entries of

A

. Assume that

A^{2} = I

Statement

1 :

A \neq I

and

A \neq - I

, then det

A = - 1

Statement

2 :

A \neq I

and

A \neq - I

, then

t r (A) \neq 0,

then which of the following is correct

Q. Let A be a

2 \times 2

matrix with real entries. Let I be the

2 \times 2

identity matrix. Denote by tr(A), the sum of diagonal entries of

A

. Assume that

A^{2} =

I.
Statement-l: If

A \neq I

and

A \neq - I

, then

det A = - 1

.
Statement-2: If

A \neq I

and

A \neq - I

, then

t_{1} {A) \neq 0

Q. Let

A

be a symmetric matrix of order

2

with integer entries. If the sum of the diagonal elements of

A^{2}

1,

then the possible number of such matrices is :

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Let A[123−5] and B=[1002] and X be a matrix such that A=BX. Then −4× sum of diagonal entries of X is,

The correct option is D 6Let X=[abcd]∴[123−5]=[1002][abcd]=[ab2c2d]∴a=1,b=2,2c=3,2d=−5∴X=[123/2−5/2]=12[243−5]−4× sum of diagonal entries =6

Let $A [\begin{matrix} 1 & 2 3 & - 5 \end{matrix}]$ and $B = [\begin{matrix} 1 & 0 0 & 2 \end{matrix}]$ and X be a matrix such that $A = B X .$ Then $- 4 \times$ sum of diagonal entries of $X$ is,