Question
Let three matrices A =
; B =
and C =
then tr(A) + tr
+ tr
+ tr
+ ....... +
=
- 6
- 9
- 12
- none
Hint:
Trace of matrix is sum of its diagonal elements from the upper left to lower right, of matrix.
Multiply the B and C using matrix multiplication and Find the matrix BC and we observe the Geometric progression with common ratio using sum upto infinite in Gp solve the value. .
The correct answer is: 6
tr(A) = trace of
= 2+1 = 3
![B C space equals space open square brackets table row 3 4 row 2 3 end table close square brackets space open square brackets table row 3 cell negative 4 end cell row cell negative 2 end cell 3 end table close square brackets space equals open square brackets table row cell 9 minus 8 end cell cell space space minus 12 plus 12 end cell row cell 6 minus 6 end cell cell negative 8 plus 9 end cell end table close square brackets
equals open square brackets table row 1 0 row 0 1 end table close square brackets space equals text I (unit matrix) end text](data:image/png;base64,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)
then tr(A) + tr
+ tr
+ tr
+ ....... + ![straight infinity](data:image/png;base64,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)
tr(A) + tr
+ tr
+ tr
+ ....... +
= tr(A) + tr
+ tr
+ tr
+ ....... + ![straight infinity](data:image/png;base64,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)
As we know
then
tr(A) + tr
+ tr
+ tr
+ ....... +
= tr(A) +
tr(A)+
tr(A) +
tr(A)+ ....... + ![straight infinity](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAKCAYAAAC9vt6cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAJufgqOgAAALNJREFUeNpjYICAUCA+A8SfgPgCELcCsTADAugB8WIgvgLEu4G4HkmOIRyI1wCxBxQvBeL/QPwciNWAOBGILwGxMZIeS6glYLCYARPUQw15CsTXgFgQi5oSIBYHMaYxYAdToIacBGIOLPJ+QOwGYkzCYcBiqAtAhuzAYkgHEIuCGEFAnIckIQ4Nk7lAzAPEh6GGXECytRXd5aCAPAp1LiiUA9BsywDig0D8AYjvA3Etw/ABAM+/JhHyx6vcAAAAZXRFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaSBtYXRodmFyaWFudD0ibm9ybWFsIj4mI3gyMjFFOzwvbWk+PC9tYXRoPvJ0D8MAAAAASUVORK5CYII=)
tr(A)( 1 +
+
+
+ ....... +
)
Here, common ratio r is
(< 1) and a = 1 the sum upto infinite = ![fraction numerator a over denominator 1 minus r end fraction](data:image/png;base64,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)
= ![3 left parenthesis fraction numerator 1 over denominator 1 minus begin display style 1 half end style end fraction right parenthesis space equals space 3 space cross times fraction numerator 1 over denominator space left parenthesis begin display style 1 half end style right parenthesis space end fraction space equals space 3 cross times space 2 space equals 6](data:image/png;base64,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)
Therefore, the value of tr(A) + tr
+ tr
+ tr
+ ....... +
= 6.
Related Questions to study
A =
then let us define a function f(x) = dt.(ATA–1) then which of the following can not be the value of
is (n ≥ 2)
A =
then let us define a function f(x) = dt.(ATA–1) then which of the following can not be the value of
is (n ≥ 2)
Let A, B, C, D be (not necessarily square) real matrices such that AT = BCD; BT = CDA; CT = DAB and DT = ABC for the matrix S = ABCD, consider the two statements.
I. S3 = S
II. S2 = S4
Let A, B, C, D be (not necessarily square) real matrices such that AT = BCD; BT = CDA; CT = DAB and DT = ABC for the matrix S = ABCD, consider the two statements.
I. S3 = S
II. S2 = S4
Let A =
, where 0 ≤ θ < 2
, then
Let A =
, where 0 ≤ θ < 2
, then
If A is matrix such that A2 + A + 2I = O, then which of the following is INCORRECT ?
(Where I is unit matrix of orde r 2 and O is null matrix of order 2)
inverse of a matrix exists when the determinant of the matrix is 0.
any matrix multiplied by the identity matrix of the same order gives the same matrix.
If A is matrix such that A2 + A + 2I = O, then which of the following is INCORRECT ?
(Where I is unit matrix of orde r 2 and O is null matrix of order 2)
inverse of a matrix exists when the determinant of the matrix is 0.
any matrix multiplied by the identity matrix of the same order gives the same matrix.
Identify the incorrect statement in respect of two square matrices A and B conformable for sum and product.
trace of a matrix is the sum of the diagonal elements of a matrix.
Identify the incorrect statement in respect of two square matrices A and B conformable for sum and product.
trace of a matrix is the sum of the diagonal elements of a matrix.
In the reaction ![3 Br subscript 2 plus 6 CO subscript 3 superscript 2 minus end superscript plus 3 straight H subscript 2 straight O not stretchy rightwards arrow 5 Br to the power of ⊖ plus BrO subscript 3 superscript ⊖ plus 6 HCO subscript 3 superscript ⊖](data:image/png;base64,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)
In the reaction ![3 Br subscript 2 plus 6 CO subscript 3 superscript 2 minus end superscript plus 3 straight H subscript 2 straight O not stretchy rightwards arrow 5 Br to the power of ⊖ plus BrO subscript 3 superscript ⊖ plus 6 HCO subscript 3 superscript ⊖](data:image/png;base64,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)
A is an involutary matrix given by A =
then inverse of
will be
an involutary matrix is one which follows the property A2= I, I = identity matrix of 3rd order.
A is an involutary matrix given by A =
then inverse of
will be
an involutary matrix is one which follows the property A2= I, I = identity matrix of 3rd order.