Question
If the rank of the matrix
is 2 then
- k =
, x =
- k =
, x ≠
- k =
, x =
- None of these
Hint:
The rank of a matrix is the maximum number of its linearly independent rows. If two rows or columns of the are in GP then the det (Determinant) of that matrix is 0.
The correct answer is: k =
, x ≠ ![fraction numerator 1 over denominator 5 end fraction](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAIJJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CoZCDI4WZDQw6BcQfwLibUBcBMQ8lBjIAsTG0IbEDSDWoIYr3YD4ILW8/IMahugA8V1SNa0DYksgZoJiD6ghQaQaFArEt4D4DxC/A+JVQGyKTwMAfKc5il4VJDgAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+NTwvbW4+PC9tZnJhYz48L21hdGg+Xdkl9QAAAABJRU5ErkJggg==)
Given, the rank of the matrix
is 2
To get rank 2 out of 3 x 3 matrix the Det of 3x3 matrix must be 0.
then if k =
then matrix det(Determinant) will be 0 independent of x as first 2 columns will be in Geometric progression and then at least one 2 x 2 should not be 0 to get the rank 2.
![open vertical bar table row 2 cell 1 minus x end cell row cell 5 over 2 end cell 1 end table close vertical bar space not equal to space 0 space space rightwards double arrow 2 space minus 5 over 2 left parenthesis 1 minus x right parenthesis space not equal to space 0 space space
rightwards double arrow fraction numerator negative 1 over denominator 2 end fraction plus fraction numerator 5 x over denominator 2 end fraction not equal to space 0 space rightwards double arrow space 5 x not equal to 1
rightwards double arrow x not equal to 1 fifth](data:image/png;base64,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)
So, k =
and ![x space not equal to 1 fifth](data:image/png;base64,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)
Related Questions to study
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If A =
, then AT + A = I2, if –
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Let A =
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If A is matrix such that A2 + A + 2I = O, then which of the following is INCORRECT ?
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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.