Question
If A =
, then AT + A = I2, if –
![theta equals n pi comma n element of Z](data:image/png;base64,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)
- θ= (2n + 1)
, n
Z
- θ=2n
+
,n
Z
- None of these
Hint:
Find the transpose of A and add it with A and compare with unit matrix of dimension 2 x2 as give to get the value of θ and generalize it .
The correct answer is: θ=2n
+
,n
Z
Given, A =
, then AT = ![open square brackets table row cell cos invisible function application theta end cell cell sin invisible function application theta end cell row cell negative sin invisible function application theta end cell cell cos invisible function application theta end cell end table close square brackets](data:image/png;base64,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)
Now, A+AT = I2 then
+
= ![open square brackets table row cell 2 cos invisible function application theta end cell 0 row 0 cell 2 cos invisible function application theta end cell end table close square brackets](data:image/png;base64,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)
=
upon comparison ![2 cos invisible function application theta space equals space 1 space space rightwards double arrow space cos invisible function application theta space equals 1 half space rightwards double arrow theta equals pi over 3 space](data:image/png;base64,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)
Therefore, θ = 2n
+
,n
Z
Related Questions to study
If A =
and B =
, then value of
for which A2 = B is:
If A =
and B =
, then value of
for which A2 = B is:
Which of the following has no action with starch solution?
Which of the following has no action with starch solution?
Let three matrices A =
; B =
and C =
then tr(A) + tr
+ tr
+ tr
+ ....... +
=
Let three matrices A =
; B =
and C =
then tr(A) + tr
+ tr
+ tr
+ ....... +
=
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,iVBORw0KGgoAAAANSUhEUgAAAWUAAAAXCAYAAADTGF7FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAABZ5JREFUeNrtXV9kllEYPybTRcYkk0wkmUkiSZIZk0mSMUmSGV3sIuk2XSWSLrpITBeTJCZdJNPdJMmYmWQSSdJFIpnkM+PrPN7ns3ef98/znD/vOfve58fDvu+83/ee5/f8Oec853zvlBL4QBNlTcs7LfuFEoFAIAiPLi1TWpaECoFAIIgHDaGgNtir5aGWj1pWtDzWMii6CoSveDCk5Y3QUAsc0/Jey9HUexB081pOia7iGxy+hrXMafmHs7rPWu5r2Zlxbate+l3LJy0vtOyJkARQflbLKur0EhNk1uh1D0euNdT9Vo7ugzi6/UIpG+l2q6SmvK+AxyxxDa5982DaNy5vrsDh2NavoVS1oGVXRtt29IMez3raxCTHRiF1pca2iR/7ygVGfEG2HtPSnXrvsJbXBIUu4A1jwhU01AF8DQpf1PK27bqzWha1jCJxrUQ6maH7eZXUhofx2i78ewk5aAfc+xV+X2jY2Nc2KXN5c52sTK/l+jX40J2C9inkogo9uX3n2iikrtTY5vqxz1zglK9VgkJdOKqoSAJsEMmlXPdFSy/x2s85o38vtg22zZDnPM8WbGauHPva3I/LW0xJmevXEIw/tXzNEWi7GmHfTWwUSldqbHP92GcucMrXPlwKlSnUrzafLmjiezMY9OsVB9g0cQY2jSMU9TsnC9qh7VHqNSTkgYgGKhv72tyPyxsVNxXtmKFNYuP6NcyG7pbMhsYrSsqcvpvYKJSu1Njm+rHPXOCErz4tE5jxTxcoBKMxFKhhE+tIW/sKdq47QAL6RCwZfGPU3b6WfOdu/L50X33XiU2TMtW+Lu7H5Y2KZ5hcLnhIbKZ+XVQ33KGSTZ4eT7a16buJjULpSo1trh/7zAVWfLUnkWsFCrUEpt0HM9qPBExADaw3wWbHP1zGLWLdKQ3O0nTN0TWhl+dc+9oOLr5460ObNnFWsr1AlzVM4LB6uY5B4MuvYQMKNm2Op947jEnyVEW25fbd1EYhdKXGNtePq8gFVnxBXeQcZvahAgJhxB1RyWbWIUdLag6pzYLPLeEscBuOUidwZjjl0RBVnEVuOkiaVPu6mCnb8NZkyGzJPbZhUrqJs60Bj34NZYIHWpZVch6VetLExrY2fbexUdW6UmOb68dV5QJTvjZNqxcICoGDz3tIyqYJYTVnKQKj0o/U6xUkibpk2eNhGR6ifMG1r235wgdv6ZnyNLNM1lrex+LXLssXJn2PwbddxzbXj7dULmgQCWwwyDB9JgTVcHNq40hL0SgH5xGpO8QQ+FcK2ieU2YZVyKTMsW9eW5k9ffFGrSlX5dexJWVO32PwbdexzfXjLZMLDuGyoEwhIOkvk2CTZ0JQDZd35m+gbWbYr8qL9unPwrI3qxjfo/wf7fKRlKn2pbTl2dMXb9TTF1mAeusXT34dS1Lm9D0G33Yd21w/jjIXwHJuPFWnGcZOXi5RCH4BcwNrIybO1PBguG7UZxL1AcBPHD+opN6WxhjqeSm1BO7D1+2H0cexFjSkNg6Mj6jsA+PpGeSy8vez06Zn+3Lvl2VPDm+uARtCx1P3HcWEPObZr0MmZZO+h/ZtH7HN9ePocsFJlWwONFCgHnWmpATRxGufqM2HrqkE+3wmxC5cQsBsYR3vczLnWqhHPcflMPT9t5anKtlAaEfrp5V/VLLLPUMYFQdUmHqzjX1NgqfInia8ucA4zlzW0a6wIXjUs1+HgIu+bxXfpsa2iR/XIRfkouiZEJ2GLjRuJ6NO9hTUy7drwVdMz4TwDXiQCRyBmehgHetkT0G9fLsWfFX1TIiYlpSXOnyGXBd7Curl27Xhq6pnQsQCSFa3VfERmq2MutlTUB/frg1fVT0TIjZ06n8eqas9BZ3v28JXBwN2hheFBoH4tvAlfIWfQcKoCA/I3iuUCMS3hS8KX/8B5Cjzr31Auh4AAAIfdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1uPjM8L21uPjxtc3ViPjxtaT5CcjwvbWk+PG1uPjI8L21uPjwvbXN1Yj48bW8+KzwvbW8+PG1uPjY8L21uPjxtc3Vic3VwPjxtaT5DTzwvbWk+PG1uPjM8L21uPjxtcm93Pjxtbj4yPC9tbj48bW8+JiN4MjIxMjs8L21vPjwvbXJvdz48L21zdWJzdXA+PG1vPis8L21vPjxtbj4zPC9tbj48bXN1Yj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+SDwvbWk+PG1uPjI8L21uPjwvbXN1Yj48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+TzwvbWk+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjE5Mjs8L21vPjxtbj41PC9tbj48bXN1cD48bWk+QnI8L21pPjxtbz4mI3gyMjk2OzwvbW8+PC9tc3VwPjxtbz4rPC9tbz48bXN1YnN1cD48bWk+QnJPPC9taT48bW4+MzwvbW4+PG1vPiYjeDIyOTY7PC9tbz48L21zdWJzdXA+PG1vPis8L21vPjxtbj42PC9tbj48bXN1YnN1cD48bWk+SENPPC9taT48bW4+MzwvbW4+PG1vPiYjeDIyOTY7PC9tbz48L21zdWJzdXA+PC9tYXRoPjejuZIAAAAASUVORK5CYII=)
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.